Question 23M.2.HL.TZ1.6
| Date | May 2023 | Marks available | [Maximum mark: 11] | Reference code | 23M.2.HL.TZ1.6 |
| Level | HL | Paper | 2 | Time zone | TZ1 |
| Command term | Calculate, Discuss, Explain, Sketch | Question number | 6 | Adapted from | N/A |
The centres of two identical fixed conducting spheres each of charge +Q are separated by a distance D. C is the midpoint of the line joining the centres of the spheres.
Sketch, on the axes, how the electric potential V due to the two charges varies with the distance r from the centre of the left charge. No numbers are required. Your graph should extend from r = 0 to r = D.
[3]
Constant, non-zero within spheres ✓
A clear, non-zero positive minimum at C ✓
Symmetric bowl shaped up curved shape in between ✓
Do not allow a bowl shaped down curve for MP3.
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
[2]
V «= 2 × » = 6.0 × 107 «V» ✓
W = «qV = 6.0 × 107 × 4.0 × 10−9 =» 0.24 «J» ✓
Allow ECF from MP1
The small positive charge q is placed a distance to the right of C. The distance is very small compared to D.
The magnitude of the net force on q is given by . Explain why the charge q will execute simple harmonic oscillations about C.
[2]
The restoring force/acceleration is opposite to the displacement/towards equilibrium / OWTTE ✓
and proportional to displacement from equilibrium / OWTTE✓
Allow discussions based on the diagram (such as towards C for towards equilibrium).
Accept F ∝ x OR a ∝ x for MP2
The mass of the charge q is 0.025 kg.
Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).
[2]
ω = OR use of F =mω2r OR F = 1.33x OR a = 53.3x ✓
«» = 7.299 «s−1»
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 and released. Discuss whether the motion of m will be the same as that of q.
[2]
the net force will no longer be a restoring force/directed towards equilibrium
OR
the gravitational force is attractive/neutral mass would be pulled towards larger masses/OWTTE ✓
«and so» no, motion will not be the same/no longer be SHM / OWTTE ✓