1. 1
   Two identical small metal spheres, P and Q, are mounted on insulating stands with their centres 0.30 m apart in air. Sphere P carries a charge of +6.0 nC and sphere Q carries a charge of −2.0 nC. The spheres can be treated as point charges.

   (a)

   What is the electric force between P and Q?

   [1 mark]

   • A1.2 × 10⁻⁶ N, repulsive
   • B1.2 × 10⁻⁶ N, attractive
   • C3.6 × 10⁻⁷ N, attractive
   • D1.3 × 10⁻¹⁶ N, attractive

   (b)

   P and Q are touched together and then returned to their original positions. What is the force between them now?

   [1 mark]

   • A4.0 × 10⁻⁷ N, repulsive
   • BZero, because the charges have neutralised
   • C4.0 × 10⁻⁷ N, attractive
   • D1.6 × 10⁻⁶ N, repulsive

   (c)

   A student says that, during contact, positive charge flowed from P to Q. Explain what actually happens, and determine the number of charged particles that move.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a version of Millikan's experiment, two horizontal metal plates are 6.0 mm apart, with the upper plate positive. A potential difference of 600 V between the plates holds a charged oil drop of mass 4.9 × 10⁻¹⁵ kg stationary between them. On other occasions, drops were found carrying charges of magnitude 3.2 × 10⁻¹⁹ C, 6.4 × 10⁻¹⁹ C, 8.0 × 10⁻¹⁹ C and 1.12 × 10⁻¹⁸ C.

   (a)

   What is the electric field strength between the plates?

   [1 mark]

   • A3.6 V m⁻¹
   • B1.0 × 10⁻⁵ V m⁻¹
   • C1.0 × 10² V m⁻¹
   • D1.0 × 10⁵ V m⁻¹

   (b)

   What is the charge on the stationary drop?

   [1 mark]

   • A+4.8 × 10⁻¹⁹ C
   • B−1.6 × 10⁻¹⁹ C
   • C−4.8 × 10⁻¹⁹ C
   • D−4.8 × 10⁻¹⁶ C

   (c)

   Explain how the charges measured in this experiment provide evidence that electric charge is quantised.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student uses a field probe to measure the electric field strength between two large, parallel metal plates in air. With the probe at the centre of the gap: for a separation of 4.0 cm and a potential difference of 200 V, E = 5.0 × 10³ V m⁻¹; for 4.0 cm and 400 V, E = 1.0 × 10⁴ V m⁻¹; for 2.0 cm and 200 V, E = 1.0 × 10⁴ V m⁻¹. With 4.0 cm and 400 V, the reading stays at 1.0 × 10⁴ V m⁻¹ as the probe is moved anywhere in the central region between the plates, but it falls to about 3 × 10³ V m⁻¹ when the probe is level with the edges of the plates.

   (a)

   Show that the student's data are consistent with E = V/d.

   [3 marks]

   (b)

   Explain, with reference to electric field lines, why the reading is constant anywhere in the central region but falls near the edges of the plates.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A teacher rubs a polythene rod with a woollen cloth, and the rod becomes negatively charged. She uses the rod, without letting it touch, to give an uncharged metal sphere on an insulating stand a positive charge. In the same lesson, the class uses a plotting compass to trace the magnetic field lines around a bar magnet and around a long solenoid carrying a steady current.

   (a)

   Explain how the rod becomes charged, and describe and explain how the teacher can use the rod to give the sphere a positive charge. Refer to conservation of charge and to the role of earthing.

   [6 marks]

   (b)

   A student writes: "Magnetic field lines are just like electric field lines: they begin on north poles and end on south poles, in the same way that electric field lines begin on positive charges and end on negative charges." Evaluate this statement, with reference to the magnetic field lines of the bar magnet and of the solenoid.

   [6 marks]

   Total for question 4: 12 marks

End of questions