Coulomb's lawAQA A-Level Physics: Subtopic test

1. 1
   Two small metal spheres in air carry charges of +3.0 nC and −5.0 nC. Their centres are 4.0 cm apart.

   (a)

   Which statement about the electrostatic forces between the two spheres is correct?

   [1 mark]

   • AThe force is repulsive and larger on the sphere with the smaller charge
   • BThe force is attractive and larger on the sphere with the larger charge
   • CThe force is attractive and has the same magnitude on both spheres
   • DThere is no force because the net charge on the two spheres is not zero

   (b)

   Which is a correct unit for the permittivity of free space, ε₀?

   [1 mark]

   • AN m² C⁻²
   • BC² N⁻¹ m⁻²
   • CN C² m⁻²
   • DC N⁻¹ m

   (c)

   Calculate the magnitude of the electrostatic force between the spheres. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a hydrogen atom an electron orbits a proton. The mean separation of the particles is 5.3 × 10⁻¹¹ m. A student compares the electrostatic and gravitational forces between them.

   (a)

   Which statement correctly describes the forces between the proton and the electron?

   [1 mark]

   • AThe electrostatic force is attractive and the gravitational force is attractive, with the electrostatic force far larger
   • BThe electrostatic force is repulsive and the gravitational force is attractive
   • CBoth forces are attractive and of similar magnitude
   • DThe electrostatic force is attractive and the gravitational force is repulsive and negligible

   (b)

   Gravity is the dominant force in the motion of planets even though it is much weaker than the electrostatic force between charged particles. What is the main reason?

   [1 mark]

   • AGravity has a longer range because it decreases more slowly than an inverse square law
   • BElectrostatic forces act only over atomic distances
   • CElectrostatic forces act only between charges of the same sign
   • DLarge bodies such as planets are electrically neutral overall, so their net electrostatic force is negligible, while gravitational forces always add

   (c)

   Calculate the ratio of the electrostatic force to the gravitational force between the proton and the electron, and state why the ratio does not depend on their separation. Use $e = 1.60 \times 10^{-19}$ C, $m_e = 9.11 \times 10^{-31}$ kg, $m_p = 1.67 \times 10^{-27}$ kg, $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$ and $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A charged metal sphere of radius 2.0 cm carries a charge of +8.0 nC. A small ball carrying −2.0 nC is held in air with its centre 10.0 cm from the centre of the sphere.

   (a)

   Calculate the magnitude of the electrostatic force between the sphere and the ball. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$.

   [3 marks]

   (b)

   The charge on the sphere is now reduced to +2.0 nC and the ball is moved to 5.0 cm from the centre of the sphere. Determine how the force compares with your answer to (a), and justify the assumptions made in using Coulomb's law here.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two small spheres, A carrying +6.0 nC and B carrying −6.0 nC, are fixed in air with their centres 0.20 m apart. A small sphere P carrying +2.0 nC is placed on the perpendicular bisector of the line AB, 0.10 m from the midpoint of AB.

   (a)

   Calculate the magnitude of the resultant electrostatic force on P and state its direction. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$.

   [6 marks]

   (b)

   The electrostatic force between a proton and an electron in an atom is about $10^{39}$ times greater than the gravitational force between them. Discuss the similarities and differences between electrostatic and gravitational forces, and explain why gravity nevertheless controls the motion of planets and stars.

   [6 marks]

   Total for question 4: 12 marks

End of questions