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
State the direction of the resultant electric field at P.
Explain why q will perform simple harmonic oscillations when it is released.
Calculate the period of oscillations of q.
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.
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.
Markscheme
«electric field at P from one charge is kQr2=kQr2=» 8.99×109×44×10-60.4828.99×109×44×10−60.482
OR
1.7168×1061.7168×106 «NC−1» ✓
« net field is » 2×1.7168×106×cos 30°=2.97×1062×1.7168×106×cos30°=2.97×106 «NC−1» ✓
directed vertically up «on plane of the page» ✓
Allow an arrow pointing up on the diagram.
force «on q» is proportional to the displacement ✓
and opposite to the displacement / directed towards equilibrium ✓
«a=Fm=»ω2x=115x0.25 ✓
T=«2πω=» 0.29 «s» ✓
Award [2] marks for a bald correct answer.
Allow ECF for MP2.
decreasing from 12 ✓
correct shape as shown ✓
Do not penalize if the graph does not touch the t axis.
12=e-5.020×106 C ✓
C=3.6×10-7 «F» ✓
Award [2] for a bald correct answer.