Electric fieldsAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Electric fields topic test

Total 54 marks

Name

Class

Date

1
Two protons in a helium nucleus are 1.7 × 10⁻¹⁵ m apart. Charge of a proton $e$ = 1.60 × 10⁻¹⁹ C, mass of a proton = 1.67 × 10⁻²⁷ kg, permittivity of free space $\varepsilon_0$ = 8.85 × 10⁻¹² F m⁻¹ and gravitational constant $G$ = 6.67 × 10⁻¹¹ N m² kg⁻². Treat the protons as point charges.
(a)
What is the magnitude of the electrostatic force between the two protons?
[1 mark]
A1.0 × 10³ N
B80 N
C1.4 × 10⁻¹³ N
D5.0 × 10²⁰ N
(b)
What is the ratio of the electrostatic force to the gravitational force between the two protons?
[1 mark]
A1.2 × 10³⁶
B1.1 × 10¹⁸
C8.1 × 10⁻³⁷
D2.1 × 10⁹
(c)
The distance between the protons is doubled. State how the ratio in part (b) changes, and explain your answer.
[2 marks]
Total for question 1: 4 marks
2
An ink droplet of mass 1.5 × 10⁻¹⁰ kg carries a charge of −2.4 × 10⁻¹² C. It passes between two parallel vertical plates 8.0 × 10⁻³ m apart, with a potential difference of 1.0 × 10³ V across them. Treat the field between the plates as uniform, and ignore the weight of the droplet.
(a)
What is the electric field strength between the plates?
[1 mark]
A1.25 × 10⁻⁵ V m⁻¹
B8.0 V m⁻¹
C1.25 × 10⁵ V m⁻¹
D1.0 × 10³ V m⁻¹
(b)
What is the magnitude of the electric force on the droplet?
[1 mark]
A2.4 × 10⁻⁹ N
B1.9 × 10⁻¹⁷ N
C5.2 × 10¹⁶ N
D3.0 × 10⁻⁷ N
(c)
Calculate the magnitude of the acceleration of the droplet, and state the direction of the force on it relative to the direction of the field.
[2 marks]
Total for question 2: 4 marks
3
An isolated metal sphere of radius 0.15 m is charged to an electric potential of +12 kV. Its charge can be considered to be at its centre. Use $1/(4\pi\varepsilon_0) = 8.99 \times 10^{9}$ N m² C⁻².
(a)
Calculate the charge on the sphere.
[3 marks]
(b)
A small particle of charge +5.0 nC is released from rest at the surface of the sphere and moves away from it along a straight line. Calculate the kinetic energy of the particle when it is 0.60 m from the centre of the sphere.
[4 marks]
Total for question 3: 7 marks
4
A gold nucleus has a charge of +79 $e$ . An alpha particle, of charge +2 $e$ and mass 6.64 × 10⁻²⁷ kg, with a kinetic energy of 5.0 MeV, is fired directly towards the gold nucleus from a very large distance away. Treat the nucleus as a stationary point charge. $e$ = 1.60 × 10⁻¹⁹ C. Use $1/(4\pi\varepsilon_0) = 8.99 \times 10^{9}$ N m² C⁻².
(a)
Explain, in terms of energy, why the alpha particle comes momentarily to rest, and calculate its distance of closest approach to the nucleus.
[6 marks]
(b)
At the distance of closest approach, 4.5 × 10⁻¹⁴ m, calculate the electric field strength due to the gold nucleus, the force on the alpha particle and the magnitude of its acceleration. State the direction of the force.
[6 marks]
Total for question 4: 12 marks
5
An isolated point charge of −2.5 nC is held in a vacuum. Use $1/(4\pi\varepsilon_0) = 8.99 \times 10^{9}$ N m² C⁻². Charge of a proton $e$ = 1.60 × 10⁻¹⁹ C.
(a)
What is the electric potential at a point 0.30 m from the charge?
[1 mark]
A+75 V
B−75 V
C−250 V
D−940 V
(b)
The distance from the charge is doubled. Which row describes the change in the magnitudes of the electric field strength $E$ and the electric potential $V$ ?
[1 mark]
A $E$ halves, $V$ halves
B $E$ halves, $V$ falls to a quarter
C $E$ falls to a quarter, $V$ halves
D $E$ falls to a quarter, $V$ falls to a quarter
(c)
A proton is released from rest at a very large distance from the charge and moves towards it. Calculate the kinetic energy of the proton, in electronvolts and in joules, when it is 0.30 m from the charge.
[2 marks]
Total for question 5: 4 marks
6
Two small spheres carrying charges of +4.0 nC and +9.0 nC are fixed in air with their centres 0.50 m apart. Treat both spheres as point charges. Use $1/(4\pi\varepsilon_0) = 8.99 \times 10^{9}$ N m² C⁻².
(a)
At what distance from the +4.0 nC sphere, along the line joining the two spheres, is the electric field strength zero?
[1 mark]
A0.25 m
B0.15 m
C0.30 m
D0.20 m
(b)
What is the magnitude of the force on the +4.0 nC sphere due to the +9.0 nC sphere?
[1 mark]
A1.3 × 10⁻⁶ N
B6.5 × 10⁻⁷ N
C3.2 × 10⁻⁷ N
D2.6 × 10⁻⁶ N
(c)
Calculate the electric field strength at the position of the +4.0 nC sphere due to the +9.0 nC sphere, and state its direction.
[2 marks]
Total for question 6: 4 marks
7
An alpha particle, of mass 6.64 × 10⁻²⁷ kg and charge +3.2 × 10⁻¹⁹ C, enters a region of uniform electric field of strength 5.0 × 10³ V m⁻¹ at right angles to the field lines. Its speed on entering is 1.5 × 10⁶ m s⁻¹. The field extends over a distance of 0.12 m in the original direction of travel of the particle. Ignore the weight of the alpha particle.
(a)
Calculate the magnitude of the acceleration of the alpha particle in the field.
[3 marks]
(b)
Calculate the sideways displacement of the particle when it leaves the field, and explain why its path in the field is a parabola.
[4 marks]
Total for question 7: 7 marks
8
In an ion thruster, singly charged xenon ions, each of charge +1.60 × 10⁻¹⁹ C and mass 2.18 × 10⁻²⁵ kg, are accelerated from rest through a potential difference of 1.2 kV between two grids 5.0 mm apart. Treat the field between the grids as uniform. Use $1/(4\pi\varepsilon_0) = 8.99 \times 10^{9}$ N m² C⁻².
(a)
Calculate the electric field strength between the grids, the force on an ion and its acceleration. Calculate also the kinetic energy of an ion as it leaves the second grid and its speed at that point.
[6 marks]
(b)
Two ions in the beam are 2.0 mm apart. Calculate the electrostatic force between them and the acceleration it would cause for one ion. Explain why a beam of ions spreads out unless it is neutralised with electrons.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).