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Date May 2022 Marks available 3 Reference code 22M.2.HL.TZ2.7
Level Higher level Paper Paper 2 Time zone 2
Command term Determine Question number 7 Adapted from N/A

Question

A metal sphere is charged positively and placed far away from other charged objects. The electric potential at a point on the surface of the sphere is 53.9 kV.

A small positively charged object moves towards the centre of the metal sphere. When the object is 2.8 m from the centre of the sphere, its speed is 3.1 m s−1. The mass of the object is 0.14 g and its charge is 2.4 × 10−8 C.

Outline what is meant by electric potential at a point.

[2]
a.

The electric potential at a point a distance 2.8 m from the centre of the sphere is 7.71 kV. Determine the radius of the sphere.

[2]
b.

Comment on the angle at which the object meets equipotential surfaces around the sphere.

[1]
c.i.

Show that the kinetic energy of the object is about 0.7 mJ.

[1]
c.ii.

Determine whether the object will reach the surface of the sphere.

[3]
c.iii.

Markscheme

the work done per unit charge ✓

In bringing a small/point/positive/test «charge» from infinity to the point ✓

 

Allow use of energy per unit charge for MP1

a.

use of Vr = constant ✓

0.40 m ✓

 

Allow [1] max if r + 2.8 used to get 0.47 m.

Allow [2] marks if they calculate Q at one potential and use it to get the distance at the other potential.

b.

90° / perpendicular ✓

c.i.

12×0.14×10-3×3.12  OR  0.67 «mJ» seen ✓

c.ii.

«p.d. between point and sphere surface = » (53.9 kV – 7.71) «kV»  OR  46.2 «kV» seen ✓

«energy required =» VQ « = 46 200 × 2.4 × 10-8» = 1.11 mJ ✓

this is greater than kinetic energy so will not reach sphere ✓

 

MP3 is for a conclusion consistent with the calculations shown.

Allow ECF from MP1

c.iii.

Examiners report

a) Well answered.

b) Generally, well answered, but there were quite a few using r + 2.8.

ci) Very few had problems to recognize the perpendicular angle

cii) Good simple calculation

ciii) Many had a good go at this, but a significant number tried to answer it based on forces.

a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
c.iii.

Syllabus sections

Additional higher level (AHL) » Topic 10: Fields » 10.2 – Fields at work
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Additional higher level (AHL) » Topic 10: Fields
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