AQA A-Level Physics: Gravitational, Electric Fields and Capacitance

A student is comparing the gravitational field of a point mass with the electric field of a point charge. Both fields obey an inverse-square law:

Field	Force law	Field strength
Gravitational	$F = \dfrac{G m_1 m_2}{r^2}$F=r2Gm1​m2​​	$g = \dfrac{GM}{r^2}$g=r2GM​
Electric	$F = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{Q_1 Q_2}{r^2}$F=4πε0​1​r2Q1​Q2​​	$E = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{Q}{r^2}$E=4πε0​1​r2Q​

Describe and explain the principal similarities and differences between these two fields. In your answer you should refer to: the way each field strength varies with distance; the existence of field strength and potential for each; the fact that one force is always attractive while the other may attract or repel; and the relative strengths of the two interactions.

(6 marks)

A small survey satellite moves in a circular orbit around a newly mapped planet. The data for the planet and the orbit are given below.

Quantity	Symbol	Value
Mass of planet	$M$M	$6.00 \times 10^{24}\ \text{kg}$6.00×1024 kg
Radius of orbit (from planet's centre)	$r$r	$8.00 \times 10^{6}\ \text{m}$8.00×106 m
Gravitational constant	$G$G	$6.67 \times 10^{-11}\ \text{N m}^{2}\,\text{kg}^{-2}$6.67×10−11 N m2kg−2

(a) By equating the gravitational force to the centripetal force, show that the orbital speed is given by $v = \sqrt{\dfrac{GM}{r}}$v=rGM​​, and hence calculate the orbital speed of the satellite. (3 marks)

(b) Calculate the period of the orbit, and give your answer in minutes to an appropriate number of significant figures. (3 marks)

A 2000 μF capacitor is charged to 10.0 V and then discharged through a fixed resistor R. A datalogger records the potential difference across the capacitor at regular intervals:

Time / s	0	10	20	40	80
Potential difference / V	10.00	7.79	6.07	3.68	1.35

The pd decays exponentially according to $V = V_0\, e^{-t/RC}$V=V0​e−t/RC.

(a) Use the table to determine the time constant of the circuit. Explain how you obtained it from the data. (2 marks)

(b) Hence calculate the resistance of R. (2 marks)

(c) Calculate the potential difference across the capacitor 60 s after the discharge begins. (1 mark)

A portable defibrillator stores energy in a capacitor and delivers it to a patient in a single pulse. The capacitor and delivery circuit have the following specification:

Quantity	Value
Capacitance, $C$C	$32\ \mu\text{F}$32 μF
Charging pd, $V$V	$2500\ \text{V}$2500 V
Resistance of patient + leads, $R$R	$50\ \Omega$50 Ω

(a) Calculate the charge stored on the capacitor and the energy it holds when fully charged. (3 marks)

(b) At the instant the pulse begins, calculate the initial discharge current through the patient. (1 mark)

(c) Calculate the time for the charge on the capacitor to fall to half its initial value. (1 mark)

Two horizontal parallel metal plates are separated by 4.0 cm of vacuum and connected to a 5000 V supply, producing a uniform electric field between them. A single proton is released from rest next to the positive plate.

Quantity	Value
Plate separation, $d$d	$4.0\ \text{cm}$4.0 cm
Potential difference, $V$V	$5000\ \text{V}$5000 V
Charge on proton, $e$e	$1.60 \times 10^{-19}\ \text{C}$1.60×10−19 C
Mass of proton, $m_p$mp​	$1.67 \times 10^{-27}\ \text{kg}$1.67×10−27 kg

(a) Calculate the electric field strength between the plates. (1 mark)

(b) Calculate the electric force on the proton and hence its initial acceleration. (3 marks)

A spacecraft moves through the gravitational field of a planet.

(a) Define gravitational field strength at a point in a field. (1 mark)

(b) Define gravitational potential at a point in a field, and explain why gravitational potential is always negative. (2 marks)