OCR A-Level Physics: Capacitors, Electric Fields and Electromagnetism

A student holds the north pole of a bar magnet just outside one end of a fixed flat coil of $N$N turns. The coil is connected to a sensitive centre-zero ammeter. The student then pushes the magnet steadily into the coil, holds it still for a moment deep inside, and finally pulls it back out at the same steady speed.

Describe and explain, using Faraday's law and Lenz's law, what the ammeter shows during each of these three stages, and explain why a force is needed to keep the magnet moving.

(6 marks)

A capacitor is charged from a supply and then allowed to discharge through a fixed resistor. The circuit values are:

Quantity	Symbol	Value
Capacitance	$C$C	2200 μF
Discharge resistance	$R$R	47 kΩ
Initial p.d. across capacitor	$V_{0}$V0​	12 V

(a) Calculate the time constant $\tau$τ of the discharge circuit. (2 marks)

(b) The capacitor discharges for 60 s. Calculate the charge remaining on the capacitor at this time. (2 marks)

(c) Calculate the energy stored in the capacitor when it is fully charged at $V_{0} = 12 \ \text{V}$V0​=12 V. (2 marks)

A capacitor is charged to 8.0 V and then discharged through a resistor of resistance 120 kΩ. A student records the p.d. $V$V across the capacitor every 10 s:

Time / s	0	10	20	30	40	50
p.d. $V$V / V	8.0	5.4	3.6	2.4	1.6	1.1

(a) Use the data to show that the discharge is exponential. (2 marks)

(b) Determine the time constant of the circuit. (2 marks)

(c) Hence calculate the capacitance of the capacitor. (1 mark)

In a research apparatus, a proton travelling at $v = 3.0 \times 10^{6} \ \text{m s}^{-1}$v=3.0×106 m s−1 enters a region of uniform magnetic field of flux density $B = 0.25 \ \text{T}$B=0.25 T. The proton's velocity is perpendicular to the field. The mass of a proton is $1.67 \times 10^{-27} \ \text{kg}$1.67×10−27 kg and its charge is $e = 1.60 \times 10^{-19} \ \text{C}$e=1.60×10−19 C.

(a) Explain why the proton follows a circular path within the field region. (1 mark)

(b) Calculate the radius of this circular path. (3 marks)

(c) State and explain what happens to the radius of the path if the proton instead enters at twice the speed. (1 mark)

Three capacitors are connected to a 9.0 V supply. A 60 μF capacitor and a 30 μF capacitor are joined in series with each other, and this series pair is connected in parallel with a 40 μF capacitor.

(a) Calculate the total capacitance of the combination. (3 marks)

(b) Hence calculate the total charge drawn from the supply. (1 mark)

(a) State what is meant by the capacitance of a capacitor, and give its SI unit. (2 marks)

(b) Two parallel metal plates are 5.0 mm apart with a potential difference of 200 V between them. Calculate the electric field strength in the uniform field between the plates. (1 mark)