1. 1
   An electron enters the gap between two horizontal parallel metal plates, midway between them, travelling horizontally at 2.0 × 10⁷ m s⁻¹. The plates are 5.0 cm long and 2.0 cm apart, in a vacuum, and there is a potential difference of 300 V between them, with the upper plate positive. The gravitational force on the electron is negligible.

   (a)

   What is the acceleration of the electron between the plates?

   [1 mark]

   • A2.6 × 10¹⁵ m s⁻², downwards
   • B2.6 × 10¹⁵ m s⁻², upwards
   • C5.3 × 10¹³ m s⁻², upwards
   • D1.4 × 10¹² m s⁻², upwards

   (b)

   Which describes the path of the electron while it is between the plates?

   [1 mark]

   • AA straight line, because the electron's horizontal speed is constant
   • BA circular arc, because the force on the electron is constant in size
   • CA parabola curving downwards
   • DA parabola curving upwards

   (c)

   Determine the vertical deflection of the electron when it leaves the plates.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A proton travelling horizontally at 3.0 × 10⁶ m s⁻¹ enters a region of uniform magnetic field of flux density 0.20 T. The field is directed vertically downwards, so it is perpendicular to the proton's velocity. The proton stays inside the field region throughout.

   (a)

   What is the magnitude of the magnetic force on the proton?

   [1 mark]

   • AZero, because the field is perpendicular to the velocity
   • B3.2 × 10⁻²⁰ N
   • C9.6 × 10⁻¹⁴ N
   • D6.0 × 10⁵ N

   (b)

   What is the radius of the proton's circular path?

   [1 mark]

   • A0.16 m
   • B8.5 × 10⁻⁵ m
   • C0.31 m
   • D6.4 m

   (c)

   Explain why the kinetic energy of the proton does not change while it moves in the magnetic field.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A beam of singly charged positive ions travels east into a region where there is a uniform electric field of 3.0 × 10⁴ V m⁻¹ directed north and a uniform magnetic field of 0.050 T directed vertically upwards. A narrow slit beyond the region lets through only ions that are not deflected. The beam contains ions with speeds of 4.0 × 10⁵ m s⁻¹, 6.0 × 10⁵ m s⁻¹ and 8.0 × 10⁵ m s⁻¹.

   (a)

   Determine which ions pass through the slit undeflected, and show that this does not depend on the charge or mass of the ions.

   [3 marks]

   (b)

   Predict, with reasons, the direction in which the ions with speeds of 4.0 × 10⁵ m s⁻¹ and 8.0 × 10⁵ m s⁻¹ are deflected, and state what would happen to negative ions with a speed of 6.0 × 10⁵ m s⁻¹.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   When a car is jump-started, two long, straight, parallel cables 1.2 cm apart carry currents of 200 A in opposite directions for a few seconds. A 0.30 m length of the pair of cables lies in the Earth's magnetic field, which has a flux density of 5.0 × 10⁻⁵ T and makes an angle of 60° with the cables.

   (a)

   Determine the force per unit length between the cables, and explain, with reference to the magnetic field of each cable, the origin and direction of the forces on the cables.

   [6 marks]

   (b)

   Compare the force on the 0.30 m length of one cable due to the Earth's magnetic field with the force on it due to the other cable, and evaluate whether the Earth's field has any significant effect on the pair of cables.

   [6 marks]

   Total for question 4: 12 marks

End of questions