Electric Fields (OCR A Level Physics)

The diagram below shows the arrangement of the 3 protons inside the nucleus of lithium-6 ()

The separation between each proton is about 1.0 × 10⁻¹⁵ m.

i) Calculate the magnitude of the repulsive electric force F experienced by the proton P.

F = .......................................... N [4]

ii) On the diagram above, draw an arrow to show the direction of the electric force F experienced by P.

[1]

iii) Explain how protons stay within the nucleus of lithium-6.

[2]

A spherical metal dome shown below is charged to a potential of −12 kV.

The dome is supported by a cylindrical plastic rod. The radius of the dome is 0.19 m.

i) Show that the magnitude of the total charge Q on the dome is 2.5 × 10⁻⁷ C.

[2]

ii) The dome discharges slowly through the plastic rod.

It takes 78 hours for the dome to completely discharge.

1. Show that the mean current I in the plastic rod is about 9 × 10⁻¹³ A.

[2]

2. The average potential difference across the plastic rod during discharge is 6000 V. The rod has cross-sectional area 1.1 × 10⁻⁴ m² and length 0.38 m. Calculate the resistivity ρ of the plastic.

ρ = ...................................... Ω m [3]

Fig. 24 shows two horizontal metal plates in a vacuum.

Fig. 24

The diagram is not drawn to scale. Electrons travelling horizontally enter the space between the charged plates and are deflected vertically.

The potential difference between the plates is 4000 V. The distance between the plates is 0.08 m. The initial speed of the electrons is 6.0 × 10⁷ m s^–1. The vertical deflection of the electrons at the far end of the plates is x.

i) Show that the vertical acceleration a of an electron between the plates is 8.8 × 10¹⁵ m s^–2.

[3]

ii) The length of each plate is 0.12 m.

Show that the time t taken by the electron to travel this length is 2.0 × 10^–9 s.

[1]

iii) Calculate the vertical deflection x of the electron.

x = ..................................................... m [2]

The arrangement shown in Fig. 24 is now used to investigate positrons emitted from a radioactive source. The speed of the positrons is also 6.0 × 10⁷ m s^–1.

The initial path of the positrons is the same as that of the electrons in Fig. 24.

On Fig. 24, sketch the path of the positrons between the plates.

[2]

Beta-minus particles (electrons) emitted from a radioactive source have a range of speeds.

Describe and explain how a uniform magnetic field can be applied in the space between the charged plates to select beta-minus particles with a specific speed. No calculations are required.

[3]

Fig. 20.1 shows a positively charged metal sphere and a negatively charged metal plate.

Fig. 20.1

On Fig. 20.1, draw a minimum of five electric field lines to show the field pattern between the sphere and the plate.

[2]

Define electric potential at a point in space.

[1]

A metal sphere is given a positive charge by connecting its surface briefly to the positive terminal of a power supply. The electric potential at the surface of the sphere is + 5.0 kV. The sphere has radius 1.5 cm.

i) Show that the charge Q on the surface of the sphere is 8.3 × 10⁻⁹ C.

[2]

ii) Fig. 20.2 shows the charged sphere from (i) suspended from a nylon thread and placed between two oppositely charged vertical plates.

Fig. 20.2 (not to scale)

The weight of the sphere is 1.7 × 10⁻² N. The string makes an angle of 4.0° with the vertical.

1. Show that the electric force on the charged sphere is 1.2 × 10⁻³ N.

[1]

2. Calculate the uniform electric field strength E between the parallel plates.

E = ................................... N C⁻¹ [2]