Electric field strengthAQA A-Level Physics: Subtopic test

1. 1
   Two horizontal metal plates in a vacuum are 0.040 m apart. They are connected to a 2.0 kV supply, producing a uniform electric field in the gap between them.

   (a)

   Calculate the magnitude of the electric field strength between the plates.

   [1 mark]

   • A5.0 × 10⁴ V m⁻¹
   • B8.0 × 10¹ V m⁻¹
   • C2.0 × 10⁻⁵ V m⁻¹
   • D2.0 × 10³ V m⁻¹

   (b)

   A particle of charge +2e, where e = 1.60 × 10⁻¹⁹ C, is placed in the gap. What is the magnitude of the electric force on it?

   [1 mark]

   • A8.0 × 10⁻¹⁵ N
   • B1.6 × 10⁻¹⁴ N
   • C6.4 × 10⁻²⁴ N
   • D3.2 × 10⁻¹⁹ N

   (c)

   The plate separation is doubled to 0.080 m while the supply is kept at 2.0 kV. Calculate the new electric field strength and state what happens to the force on a given charge in the gap.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A small metal sphere carries a charge of +4.0 nC. Its charge may be treated as a point charge at its centre, and the sphere is isolated in air (take the permittivity of air as that of free space, ε₀ = 8.85 × 10⁻¹² F m⁻¹).

   (a)

   What is the magnitude of the electric field strength at a point 0.25 m from the centre of the sphere?

   [1 mark]

   • A1.4 × 10² V m⁻¹
   • B7.2 × 10³ V m⁻¹
   • C5.8 × 10² V m⁻¹
   • D2.3 × 10³ V m⁻¹

   (b)

   The distance from the centre of the sphere is doubled. How does the field strength change?

   [1 mark]

   • AIt decreases to one half of its value
   • BIt increases to twice its value
   • CIt increases to four times its value
   • DIt decreases to one quarter of its value

   (c)

   Explain, with reference to field lines, why the field strength decreases with distance from the sphere.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a cathode ray tube, an electron travelling horizontally at 2.0 × 10⁷ m s⁻¹ enters the gap between two horizontal parallel plates. The plates are 0.050 m long and 0.040 m apart, and there is a uniform field of 1.5 × 10⁴ V m⁻¹ directed vertically downwards between them. Ignore gravity and edge effects. The electron has charge −1.60 × 10⁻¹⁹ C and mass 9.11 × 10⁻³¹ kg.

   (a)

   Calculate the magnitude of the vertical acceleration of the electron while it is between the plates.

   [3 marks]

   (b)

   Calculate the vertical displacement of the electron as it leaves the plates, and state the direction of the deflection and the shape of the path between the plates.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Students are comparing the uniform field between a pair of parallel plates with the radial field around a point charge. The plates are separated by 0.12 m and connected to a 600 V supply. The point charge is +2.0 nC. Use ε₀ = 8.85 × 10⁻¹² F m⁻¹.

   (a)

   Show that the electric field strength between the plates is given by E = V/d, starting from the work done in moving a charge Q between the plates.

   [6 marks]

   (b)

   Calculate the field strength between the plates and the field strength at 0.10 m from the point charge. Compare the two types of field and determine the distance from the point charge at which its field strength equals that between the plates.

   [6 marks]

   Total for question 4: 12 marks

End of questions