D. Fields

A satellite in a circular orbit around the Earth needs to reduce its orbital radius.

What is the work done by the satellite rocket engine and the change in kinetic energy resulting from this shift in orbital height?

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Estimate the escape speed of the spacecraft from the planet–star system.

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Satellite X is in orbit around the Earth. An identical satellite Y is in a higher orbit. What is correct for the total energy and the kinetic energy of the satellite Y compared with satellite X?

The gravitational potential is $V$ at a distance $R$ above the surface of a spherical planet of radius $R$ and uniform density. What is the gravitational potential a distance $2R$ above the surface of the planet?

A. $\frac{V}{4}$

B. $\frac{4V}{9}$

C. $\frac{V}{2}$

D. $\frac{2V}{3}$

A satellite orbits planet $\text{X}$ with a speed $v_{\text{X}}$ at a distance $\text{r}$ from the centre of planet $\text{X}$. Another satellite orbits planet $\text{Y}$ at a speed of $v_{\text{y}}$ at a distance $\text{r}$ from the centre of planet $\text{Y}$. The mass of planet $\text{X}$ is $M$ and the mass of planet $\text{Y}$ is $4M$. What is the ratio of $\frac{v_{\text{X}}}{v_{\text{y}}}$?

A.  0.25

B.  0.5

C.  2.0

D.  4.0

Planet X has a gravitational field strength of $18 \mathrm{N} {\mathrm{kg}}^{-1}$ at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?

A.  $6 \mathrm{m} {\mathrm{s}}^{-2}$

B.  $18 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $54 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $162 \mathrm{m} {\mathrm{s}}^{-2}$

Which is the definition of gravitational field strength at a point?

A. The sum of the gravitational fields created by all masses around the point

B. The gravitational force per unit mass experienced by a small point mass at that point

C. $G\frac{M}{r^2}$, where $M$ is the mass of a planet and $r$ is the distance from the planet to the point

D. The resultant force of gravitational attraction on a mass at that point

An object of mass $m$ released from rest near the surface of a planet has an initial acceleration $z$. What is the gravitational field strength near the surface of the planet?

A.  $z$

B.  $\frac{z}{m}$

C.  $mz$

D.  $\frac{m}{z}$

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

The escape speed from a planet of radius R is v_esc. A satellite orbits the planet at a distance R from the surface of the planet. What is the orbital speed of the satellite?

A. $\frac{1}{2}{v}_{\text{esc}}$

B. $\frac{\sqrt{2}}{2}{v}_{\text{esc}}$

C. $\sqrt{2}{v}_{\text{esc}}$

D. $2v_{\text{esc}}$

The gravitational field strength at the surface of a planet of radius R is $g$. A satellite is moving in a circular orbit a distance R above the surface of the planet. What is the magnitude of the acceleration of the satellite?

A.  $0$

B.  $\frac{g}{4}$

C.  $\frac{g}{2}$

D.  $g$

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit of radius $r$. What is the work that must be done on the satellite to increase its orbital radius to $2r$?

A.  $\frac{GMm}{r}$

B.  $\frac{GMm}{2r}$

C.  $\frac{GMm}{4r}$

D.  $\frac{GMm}{8r}$

P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is F. What is the force exerted by the planet on Q?

A.  F

B.  2F

C.  4F

D.  8F

An object of mass $m$ is launched from the surface of the Earth. The Earth has a mass $M$ and radius $r$. The acceleration due to gravity at the surface of the Earth is $g$. What is the escape speed of the object from the surface of the Earth?

A.  $\sqrt{gr}$

B.  $\sqrt{2gr}$

C.  $\sqrt{2Mgr}$

D.  $\sqrt{2mgr}$

A satellite is orbiting Earth in a circular path at constant speed. Three statements about the resultant force on the satellite are:

I.   It is equal to the gravitational force of attraction on the satellite.
II.  It is equal to the mass of the satellite multiplied by its acceleration.
III. It is equal to the centripetal force on the satellite.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The centre of the Earth and the Moon are a distance $D$ apart. There is a point X between them where their gravitational fields cancel out. The distance from the centre of the Earth to X is $d$. The mass of the Earth is $M_{\text{E}}$ and the mass of the Moon is $M_{\text{M}}$.

What is correct at X?

A.  $\frac{M_{\text{E}}}{d}=\frac{M_{\text{M}}}{D-d}$

B.  $\frac{M_{\text{E}}}{D-d}=\frac{M_{\text{M}}}{d}$

C.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{{\left(D-d\right)}^2}$

D.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{D^2-d^2}$

Show that the kinetic energy of the satellite in orbit is about 2 × 10¹⁰ J.

Determine the minimum energy required to launch the satellite. Ignore the original kinetic energy of the satellite due to Earth’s rotation.

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

A space probe moves in a circular orbit around Earth. The kinetic energy of the probe is $E$.

The probe will reach the escape speed when its kinetic energy is increased at least to:

A.  $\sqrt{2}E$

B.  $2E$

C.  $2\sqrt{2}E$

D.  $4E$

What is the escape speed from the surface of a planet of radius $r$ that has an acceleration of gravity $g$ at its surface?

A.  $\sqrt{\frac{g}{r}}$

B.  $\sqrt{gr}$

C.  $\sqrt{\frac{2g}{r}}$

D.  $\sqrt{2gr}$

Planets X and Y move in circular orbits around the same star.

The orbital period of planet Y is twice the orbital period of planet X. The orbital radius of planet X is $R$.

What is the orbital radius of planet Y?

A.  $\sqrt[3]{2}R$

B.  $\sqrt[3]{4}R$

C.  $2R$

D.  $4R$

Kepler’s Third law relates the orbital period $T$ of a planet about its sun to its orbital radius $r$. The mass of the Sun is $M$.

What is a correct algebraic form of the law?

A.  $T=\frac{2\mathrm{\pi }{r}^{1.5}}{{\left(GM\right)}^{0.5}}$

B.  $T=\frac{2\mathrm{\pi }{r}^{1.5}}{GM}$

C.  $T=\frac{4\mathrm{\pi }{r}^{0.67}}{{\left(GM\right)}^2}$

D.  $T=\frac{4\mathrm{\pi }{r}^{0.67}}{GM}$

orbital speed;

The radius of the dwarf planet Pluto is 1.19 x 10⁶ m. The acceleration due to gravity at its surface is 0.617 m s⁻².

Determine the escape speed for an object at the surface of Pluto.

Pluto rotates about an axis through its centre. Its rotation is in the opposite sense to that of the Earth, i.e. from east to west.

Explain the advantage of an object launching from the equator of Pluto and travelling to the west.

The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance $x$ and released. Discuss whether the motion of m will be the same as that of q.

Determine $\frac{g_{\mathrm{M}}}{g_{\mathrm{P}}}$.

State and explain the magnitude of the resultant gravitational field strength at O.

Outline why the graph between P and O is negative.

Show that the gravitational potential V_P at the surface of P due to the mass of P is given by V_P = −g_PR_P where R_P is the radius of the planet.

The gravitational potential due to the mass of M at the surface of P can be assumed to be negligible.

Estimate, using the graph, the gravitational potential at the surface of M due to the mass of M.

Draw on the axes the variation of gravitational potential between O and M.

Two isolated point masses, P of mass m and Q of mass 2m, are separated by a distance 3d. X is a point a distance d from P and 2d from Q.

What is the net gravitational field strength at X and the net gravitational potential at X?

The escape speed from the surface of earth is v_esc. The radius of earth is R. A satellite of mass m is in orbit at a height $\frac{R}{4}$ above the surface of the Earth. What is the energy required to move the satellite to infinity?

A.  $\frac{\mathrm{m}{v^2}_{\mathrm{esc}}}{5}$

B.  $\frac{2\mathrm{m}{v^2}_{\mathrm{esc}}}{5}$

C.  $\mathrm{m}{v^2}_{\mathrm{esc}}$

D.  $2\mathrm{m}{v^2}_{\mathrm{esc}}$

The radius of the Earth is R. A satellite is launched to a height h = $\frac{R}{4}$ above the Earth’s surface.

What is $\frac{\mathrm{gravitational} \mathrm{force} \mathrm{on} \mathrm{satellite} \mathrm{at} \mathrm{the} \mathrm{surface}}{\mathrm{gravitational} \mathrm{force} \mathrm{on} \mathrm{satellite} \mathrm{at} \mathrm{height} h}$?

A.  $\frac{4}{5}$

B.  $\frac{16}{25}$

C.  $\frac{25}{16}$

D.  $\frac{5}{4}$

The mass of Mars is about ten times that of the Moon. The radius of Mars is about twice that of the Moon.

What is the $\frac{\mathrm{escape} \mathrm{speed} \mathrm{from} \mathrm{Mars}}{\mathrm{Moon}}$?

A.  $\sqrt{5}$

B.  2$\sqrt{5}$

C.  5

D.  25

An asteroid (minor planet) orbits the Sun in a circular orbit of radius 4.5 × 10⁸ km. The radius of Earth’s orbit is 1.5 × 10⁸ km. Calculate, in years, the orbital period of the asteroid.

Show that $k=\frac{1}{GM}$.

The table gives data relating to the two moons of Mars.

Determine r for Deimos.

 Determine the mass of Mars.

Show that $T\propto r^{\frac{3}{2}}$ for the planets in a solar system where $T$ is the orbital period of a planet and $r$ is the radius of circular orbit of planet about its sun.

Outline what is meant by one astronomical unit (1 AU)

Pluto is a dwarf planet of the Sun that orbits at a distance of 5.9 × 10⁹ km from the Sun. Determine, in years, the orbital period of Pluto.

escape speed from its orbit.

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

A satellite in a circular orbit around the Earth needs to reduce its orbital radius.

What is the work done by the satellite rocket engine and the change in kinetic energy resulting from this shift in orbital height?

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Estimate the escape speed of the spacecraft from the planet–star system.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Estimate the escape speed of the spacecraft from the planet–star system.

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Calculate, for the surface of $\text{Io}$, the gravitational field strength g_Io due to the mass of $\text{Io}$. State an appropriate unit for your answer.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Satellite X is in orbit around the Earth. An identical satellite Y is in a higher orbit. What is correct for the total energy and the kinetic energy of the satellite Y compared with satellite X?

The gravitational potential is $V$ at a distance $R$ above the surface of a spherical planet of radius $R$ and uniform density. What is the gravitational potential a distance $2R$ above the surface of the planet?

A. $\frac{V}{4}$

B. $\frac{4V}{9}$

C. $\frac{V}{2}$

D. $\frac{2V}{3}$

A satellite orbits planet $\text{X}$ with a speed $v_{\text{X}}$ at a distance $\text{r}$ from the centre of planet $\text{X}$. Another satellite orbits planet $\text{Y}$ at a speed of $v_{\text{y}}$ at a distance $\text{r}$ from the centre of planet $\text{Y}$. The mass of planet $\text{X}$ is $M$ and the mass of planet $\text{Y}$ is $4M$. What is the ratio of $\frac{v_{\text{X}}}{v_{\text{y}}}$?

A.  0.25

B.  0.5

C.  2.0

D.  4.0

Planet X has a gravitational field strength of $18 \mathrm{N} {\mathrm{kg}}^{-1}$ at its surface. Planet Y has the same density as X but three times the radius of X. What is the gravitational field strength at the surface of Y?

A.  $6 \mathrm{m} {\mathrm{s}}^{-2}$

B.  $18 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $54 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $162 \mathrm{m} {\mathrm{s}}^{-2}$

Which is the definition of gravitational field strength at a point?

A. The sum of the gravitational fields created by all masses around the point

B. The gravitational force per unit mass experienced by a small point mass at that point

C. $G\frac{M}{r^2}$, where $M$ is the mass of a planet and $r$ is the distance from the planet to the point

D. The resultant force of gravitational attraction on a mass at that point

An object of mass $m$ released from rest near the surface of a planet has an initial acceleration $z$. What is the gravitational field strength near the surface of the planet?

A.  $z$

B.  $\frac{z}{m}$

C.  $mz$

D.  $\frac{m}{z}$

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

The escape speed from a planet of radius R is v_esc. A satellite orbits the planet at a distance R from the surface of the planet. What is the orbital speed of the satellite?

A. $\frac{1}{2}{v}_{\text{esc}}$

B. $\frac{\sqrt{2}}{2}{v}_{\text{esc}}$

C. $\sqrt{2}{v}_{\text{esc}}$

D. $2v_{\text{esc}}$

The gravitational field strength at the surface of a planet of radius R is $g$. A satellite is moving in a circular orbit a distance R above the surface of the planet. What is the magnitude of the acceleration of the satellite?

A.  $0$

B.  $\frac{g}{4}$

C.  $\frac{g}{2}$

D.  $g$

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit of radius $r$. What is the work that must be done on the satellite to increase its orbital radius to $2r$?

A.  $\frac{GMm}{r}$

B.  $\frac{GMm}{2r}$

C.  $\frac{GMm}{4r}$

D.  $\frac{GMm}{8r}$

P and Q are two moons of equal densities orbiting a planet. The orbital radius of P is twice the orbital radius of Q. The volume of P is half that of Q. The force exerted by the planet on P is F. What is the force exerted by the planet on Q?

A.  F

B.  2F

C.  4F

D.  8F

An object of mass $m$ is launched from the surface of the Earth. The Earth has a mass $M$ and radius $r$. The acceleration due to gravity at the surface of the Earth is $g$. What is the escape speed of the object from the surface of the Earth?

A.  $\sqrt{gr}$

B.  $\sqrt{2gr}$

C.  $\sqrt{2Mgr}$

D.  $\sqrt{2mgr}$

A satellite is orbiting Earth in a circular path at constant speed. Three statements about the resultant force on the satellite are:

I.   It is equal to the gravitational force of attraction on the satellite.
II.  It is equal to the mass of the satellite multiplied by its acceleration.
III. It is equal to the centripetal force on the satellite.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The centre of the Earth and the Moon are a distance $D$ apart. There is a point X between them where their gravitational fields cancel out. The distance from the centre of the Earth to X is $d$. The mass of the Earth is $M_{\text{E}}$ and the mass of the Moon is $M_{\text{M}}$.

What is correct at X?

A.  $\frac{M_{\text{E}}}{d}=\frac{M_{\text{M}}}{D-d}$

B.  $\frac{M_{\text{E}}}{D-d}=\frac{M_{\text{M}}}{d}$

C.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{{\left(D-d\right)}^2}$

D.  $\frac{M_E}{d^2}=\frac{M_{\text{M}}}{D^2-d^2}$

Show that the kinetic energy of the satellite in orbit is about 2 × 10¹⁰ J.

Determine the minimum energy required to launch the satellite. Ignore the original kinetic energy of the satellite due to Earth’s rotation.

Show that the kinetic energy of the satellite in orbit is about 2 × 10¹⁰ J.

Determine the minimum energy required to launch the satellite. Ignore the original kinetic energy of the satellite due to Earth’s rotation.

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

A space probe moves in a circular orbit around Earth. The kinetic energy of the probe is $E$.

The probe will reach the escape speed when its kinetic energy is increased at least to:

A.  $\sqrt{2}E$

B.  $2E$

C.  $2\sqrt{2}E$

D.  $4E$

What is the escape speed from the surface of a planet of radius $r$ that has an acceleration of gravity $g$ at its surface?

A.  $\sqrt{\frac{g}{r}}$

B.  $\sqrt{gr}$

C.  $\sqrt{\frac{2g}{r}}$

D.  $\sqrt{2gr}$

Planets X and Y move in circular orbits around the same star.

The orbital period of planet Y is twice the orbital period of planet X. The orbital radius of planet X is $R$.

What is the orbital radius of planet Y?

A.  $\sqrt[3]{2}R$

B.  $\sqrt[3]{4}R$

C.  $2R$

D.  $4R$

Kepler’s Third law relates the orbital period $T$ of a planet about its sun to its orbital radius $r$. The mass of the Sun is $M$.

What is a correct algebraic form of the law?

A.  $T=\frac{2\mathrm{\pi }{r}^{1.5}}{{\left(GM\right)}^{0.5}}$

B.  $T=\frac{2\mathrm{\pi }{r}^{1.5}}{GM}$

C.  $T=\frac{4\mathrm{\pi }{r}^{0.67}}{{\left(GM\right)}^2}$

D.  $T=\frac{4\mathrm{\pi }{r}^{0.67}}{GM}$

orbital speed;

The radius of the dwarf planet Pluto is 1.19 x 10⁶ m. The acceleration due to gravity at its surface is 0.617 m s⁻².

Determine the escape speed for an object at the surface of Pluto.

Pluto rotates about an axis through its centre. Its rotation is in the opposite sense to that of the Earth, i.e. from east to west.

Explain the advantage of an object launching from the equator of Pluto and travelling to the west.

The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance $x$ and released. Discuss whether the motion of m will be the same as that of q.

The charges Q are replaced by neutral masses M and the charge q by a neutral mass m. The mass m is displaced away from C by a small distance $x$ and released. Discuss whether the motion of m will be the same as that of q.

Determine $\frac{g_{\mathrm{M}}}{g_{\mathrm{P}}}$.

State and explain the magnitude of the resultant gravitational field strength at O.

Outline why the graph between P and O is negative.

Show that the gravitational potential V_P at the surface of P due to the mass of P is given by V_P = −g_PR_P where R_P is the radius of the planet.

The gravitational potential due to the mass of M at the surface of P can be assumed to be negligible.

Estimate, using the graph, the gravitational potential at the surface of M due to the mass of M.

Draw on the axes the variation of gravitational potential between O and M.

Determine $\frac{g_{\mathrm{M}}}{g_{\mathrm{P}}}$.

State and explain the magnitude of the resultant gravitational field strength at O.

Outline why the graph between P and O is negative.

Show that the gravitational potential V_P at the surface of P due to the mass of P is given by V_P = −g_PR_P where R_P is the radius of the planet.

The gravitational potential due to the mass of M at the surface of P can be assumed to be negligible.

Estimate, using the graph, the gravitational potential at the surface of M due to the mass of M.

Draw on the axes the variation of gravitational potential between O and M.

Two isolated point masses, P of mass m and Q of mass 2m, are separated by a distance 3d. X is a point a distance d from P and 2d from Q.

What is the net gravitational field strength at X and the net gravitational potential at X?

The escape speed from the surface of earth is v_esc. The radius of earth is R. A satellite of mass m is in orbit at a height $\frac{R}{4}$ above the surface of the Earth. What is the energy required to move the satellite to infinity?

A.  $\frac{\mathrm{m}{v^2}_{\mathrm{esc}}}{5}$

B.  $\frac{2\mathrm{m}{v^2}_{\mathrm{esc}}}{5}$

C.  $\mathrm{m}{v^2}_{\mathrm{esc}}$

D.  $2\mathrm{m}{v^2}_{\mathrm{esc}}$

The radius of the Earth is R. A satellite is launched to a height h = $\frac{R}{4}$ above the Earth’s surface.

What is $\frac{\mathrm{gravitational} \mathrm{force} \mathrm{on} \mathrm{satellite} \mathrm{at} \mathrm{the} \mathrm{surface}}{\mathrm{gravitational} \mathrm{force} \mathrm{on} \mathrm{satellite} \mathrm{at} \mathrm{height} h}$?

A.  $\frac{4}{5}$

B.  $\frac{16}{25}$

C.  $\frac{25}{16}$

D.  $\frac{5}{4}$

The mass of Mars is about ten times that of the Moon. The radius of Mars is about twice that of the Moon.

What is the $\frac{\mathrm{escape} \mathrm{speed} \mathrm{from} \mathrm{Mars}}{\mathrm{Moon}}$?

A.  $\sqrt{5}$

B.  2$\sqrt{5}$

C.  5

D.  25

An asteroid (minor planet) orbits the Sun in a circular orbit of radius 4.5 × 10⁸ km. The radius of Earth’s orbit is 1.5 × 10⁸ km. Calculate, in years, the orbital period of the asteroid.

An asteroid (minor planet) orbits the Sun in a circular orbit of radius 4.5 × 10⁸ km. The radius of Earth’s orbit is 1.5 × 10⁸ km. Calculate, in years, the orbital period of the asteroid.

Show that $k=\frac{1}{GM}$.

The table gives data relating to the two moons of Mars.

Determine r for Deimos.

 Determine the mass of Mars.

Show that $k=\frac{1}{GM}$.

The table gives data relating to the two moons of Mars.

Determine r for Deimos.

 Determine the mass of Mars.

Show that $T\propto r^{\frac{3}{2}}$ for the planets in a solar system where $T$ is the orbital period of a planet and $r$ is the radius of circular orbit of planet about its sun.

Outline what is meant by one astronomical unit (1 AU)

Pluto is a dwarf planet of the Sun that orbits at a distance of 5.9 × 10⁹ km from the Sun. Determine, in years, the orbital period of Pluto.

Show that $T\propto r^{\frac{3}{2}}$ for the planets in a solar system where $T$ is the orbital period of a planet and $r$ is the radius of circular orbit of planet about its sun.

Outline what is meant by one astronomical unit (1 AU)

Pluto is a dwarf planet of the Sun that orbits at a distance of 5.9 × 10⁹ km from the Sun. Determine, in years, the orbital period of Pluto.

escape speed from its orbit.

The radius of the dwarf planet Pluto is 1.19 x 10⁶ m. The acceleration due to gravity at its surface is 0.617 m s⁻².

Determine the escape speed for an object at the surface of Pluto.

Pluto rotates about an axis through its centre. Its rotation is in the opposite sense to that of the Earth, i.e. from east to west.

Explain the advantage of an object launching from the equator of Pluto and travelling to the west.

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

A charged sphere in a gravitational field is initially stationary between two parallel metal plates. There is a potential difference V between the plates.

Three changes can be made:

I.   Increase the separation of the metal plates
II.  Increase V
III. Apply a magnetic field into the plane of the paper

What changes made separately will cause the charged sphere to accelerate?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Determine the force on Q at the instant it is released.

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

Show that the charge on the surface of the sphere is +18 μC.

Predict the charge on each sphere.

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

Explain why the electric potential decreases from A to B.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Calculate the electric potential difference between points A and B.

Determine the charge $Q$ of the sphere.

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.

Outline which of the two points has the larger electric potential.

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.

The magnetic field due to P at Q is $X$. What is the magnitude of the resultant magnetic field at Q due to both wires?

A.  $\frac{X}{2}$

B.  $X$

C.  $X\sqrt{2}$

D.  $2X$

A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

A charged sphere in a gravitational field is initially stationary between two parallel metal plates. There is a potential difference V between the plates.

Three changes can be made:

I.   Increase the separation of the metal plates
II.  Increase V
III. Apply a magnetic field into the plane of the paper

What changes made separately will cause the charged sphere to accelerate?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Determine the force on Q at the instant it is released.

Determine the force on Q at the instant it is released.

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

Show that the charge on the surface of the sphere is +18 μC.

Predict the charge on each sphere.

Show that the charge on the surface of the sphere is +18 μC.

Predict the charge on each sphere.

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

Explain why the electric potential decreases from A to B.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Calculate the electric potential difference between points A and B.

Determine the charge $Q$ of the sphere.

Explain why the electric potential decreases from A to B.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Calculate the electric potential difference between points A and B.

Determine the charge $Q$ of the sphere.

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.

Outline which of the two points has the larger electric potential.

The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.

Outline which of the two points has the larger electric potential.

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.

The magnetic field due to P at Q is $X$. What is the magnitude of the resultant magnetic field at Q due to both wires?

A.  $\frac{X}{2}$

B.  $X$

C.  $X\sqrt{2}$

D.  $2X$

A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

A. $\frac{W}{2}$

B. W

C. 2W

D. 4W

Show that the radius of the path is about 6 cm.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

A beam of negative ions flows in the plane of the page through the magnetic field due to two bar magnets.

What is the direction in which the negative ions will be deflected?

A. Out of the page $\odot$

B. Into the page X

C. Up the page ↑

D. Down the page ↓

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two long parallel wires X and Y carry equal currents I. The magnetic force exerted per unit length of each wire is $F$.

The current in X is halved and the current in Y is doubled. What is the force per unit length of each wire after the change?

Just before the loop is about to completely exit the region of magnetic field, the loop moves with constant terminal speed v.

The following data is available:

Determine, in m s⁻¹ the terminal speed v.

An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A.  $\sqrt{\frac{2eV}{m_e}}$

B.  $\frac{eV}{m_e}$

C.  $\frac{2eV}{m_e}$

D.  $\sqrt{\frac{2V}{m_e}}$

State and explain the magnitude of the force on a length of 0.50 m of wire Q due to the current in P.

Calculate the current in wire Q.

State the fundamental SI units for permeability of free space, ${\mu }_0$.

magnitude of the net force acting on the loop;

Determine the magnetic force acting on the 15 Ω wire due to the current in the 30 Ω wire.

The magnetic field strength of Earth’s field at the location of the wires is 45 μT.

Discuss the assumption made in this question.

Draw the magnetic field lines due to A.

Both wires are 7.5 m long and are 0.25 m apart. The current in both wires is 12 A. Determine the force that acts on one wire due to the other.

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

A. $\frac{W}{2}$

B. W

C. 2W

D. 4W

Show that the radius of the path is about 6 cm.

Show that the radius of the path is about 6 cm.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.

A beam of negative ions flows in the plane of the page through the magnetic field due to two bar magnets.

What is the direction in which the negative ions will be deflected?

A. Out of the page $\odot$

B. Into the page X

C. Up the page ↑

D. Down the page ↓

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two long parallel wires P and Q are a distance d apart. They each carry a current.

A magnetic force per unit length $F$ acts on P due to Q.

The distance between the wires is increased to 2d and the current in Q is decreased to $\frac{I}{2}$.

What is the magnetic force per unit length that acts on P due to Q after the changes?

A.  $\frac{F}{8}$

B.  $\frac{F}{4}$

C.  $\frac{F}{2}$

D.  $F$

Two long parallel wires X and Y carry equal currents I. The magnetic force exerted per unit length of each wire is $F$.

The current in X is halved and the current in Y is doubled. What is the force per unit length of each wire after the change?

Just before the loop is about to completely exit the region of magnetic field, the loop moves with constant terminal speed v.

The following data is available:

Determine, in m s⁻¹ the terminal speed v.

Just before the loop is about to completely exit the region of magnetic field, the loop moves with constant terminal speed v.

The following data is available: