10.1 – Describing fields

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

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

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

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.  $E\sqrt{x^2 + y^2}$

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 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.  $\frac{m}{z}$

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.  $\frac{m}{z}$

Four identical, positive, point charges of magnitude Q are placed at the vertices of a square of side 2d. What is the electric potential produced at the centre of the square by the four charges?

A.     0

B.     $\frac{4kQ}{d}$

C.     $\frac{\sqrt{2}kQ}{d}$

D.     $\frac{2\sqrt{2}kQ}{d}$

Four identical, positive, point charges of magnitude Q are placed at the vertices of a square of side 2d. What is the electric potential produced at the centre of the square by the four charges?

A.     0

B.     $\frac{4kQ}{d}$

C.     $\frac{\sqrt{2}kQ}{d}$

D.     $\frac{2\sqrt{2}kQ}{d}$

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

A parallel-plate capacitor is fully charged using a battery.

The capacitor has a capacitance C and a charge Q. The plates X and Y of the capacitor are a distance d apart. Edge effects are negligible.

Three statements about the fully charged capacitor are:

I.    The electric field strength between the plates is $\frac{Q}{Cd}$.

II.   The electric field lines are at right angles to the plates.

III.  The equipotential surfaces are parallel to the plates.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A parallel-plate capacitor is fully charged using a battery.

The capacitor has a capacitance C and a charge Q. The plates X and Y of the capacitor are a distance d apart. Edge effects are negligible.

Three statements about the fully charged capacitor are:

I.    The electric field strength between the plates is $\frac{Q}{Cd}$.

II.   The electric field lines are at right angles to the plates.

III.  The equipotential surfaces are parallel to the plates.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

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.

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.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

Show that V = –g(R + h).

Show that V = –g(R + h).

Show that V = –g(R + h).

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

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 $\frac{Q}{q}$.

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 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

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

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?

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 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 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

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

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

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

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