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Date November 2021 Marks available 2 Reference code 21N.2.HL.TZ0.3
Level Higher level Paper Paper 2 Time zone 0 - no time zone
Command term Explain Question number 3 Adapted from N/A

Question

Two equal positive fixed point charges Q = +44 μC and point P are at the vertices of an equilateral triangle of side 0.48 m.

Point P is now moved closer to the charges.

A point charge q = −2.0 μC and mass 0.25 kg is placed at P. When x is small compared to d, the magnitude of the net force on q is F ≈ 115x.

An uncharged parallel plate capacitor C is connected to a cell of emf 12 V, a resistor R and another resistor of resistance 20 MΩ.

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

[2]
a.i.

State the direction of the resultant electric field at P.

[1]
a.ii.

Explain why q will perform simple harmonic oscillations when it is released.

[2]
b.i.

Calculate the period of oscillations of q.

[2]
b.ii.

At t = 0, the switch is connected to X. On the axes, draw a sketch graph to show the variation with time of the voltage VR across R.

[2]
c.i.

The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage Vc drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.

[2]
c.ii.

Markscheme

«electric field at P from one charge is kQr2=» 8.99×109×44×10-60.482

OR

1.7168×106 «NC−1» ✓


« net field is » 2×1.7168×106×cos30°=2.97×106 «NC−1» ✓

a.i.

directed vertically up «on plane of the page» ✓

 

Allow an arrow pointing up on the diagram.

a.ii.

force «on q» is proportional to the displacement ✓

and opposite to the displacement / directed towards equilibrium ✓

b.i.

«a=Fm=»ω2x=115x0.25 ✓

T=«2πω=» 0.29«s» ✓

 

Award [2] marks for a bald correct answer.

Allow ECF for MP2.

b.ii.

decreasing from 12 ✓

correct shape as shown ✓

 

Do not penalize if the graph does not touch the t axis.

c.i.

12=e-5.020×106 C ✓

C=3.6×10-7 «F» ✓

 

Award [2] for a bald correct answer.

c.ii.

Examiners report

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

Syllabus sections

Additional higher level (AHL) » Topic 9: Wave phenomena » 9.1 – Simple harmonic motion
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