Figure 3 shows an arrangement used to investigate the repulsive forces between two identical charged conducting spheres - AQA - A-Level Physics - Question 4 - 2019 - Paper 2

Labelled arrows should indicate:

1. The electrostatic repulsive force acting horizontally away from sphere A due to the charge on sphere A.
2. The weight of sphere B acting downwards due to gravity.
3. The tension in the thread acting upwards at an angle.

One problem could be the difficulty in accurately measuring the distance d due to the movement of the spheres. A possible solution is to use transparent rulers or laser distance measuring devices that minimize the influence of external forces.

The electrostatic force (F) can be calculated using Coulomb's law:

$F = \frac{k \cdot |q_1 \cdot q_2|}{r^2}$

Where:

• $k = 8.99 \times 10^9 \, N \, m^2/C^2$,
• $q_1 = q_2 = 52 \times 10^{-9} C$ (the charge on each sphere),
• $r = 0.040 m$ (the distance between the centers of the spheres).

Substituting the values gives:

$F = \frac{(8.99 \times 10^9) \cdot (52 \times 10^{-9})^2}{(0.040)^2} \approx 4 \times 10^{-3} N$

Given that the angle is 7° and both the gravitational force and electrostatic force are in balance, this small angle indicates a relatively small force is applied. The measurement is consistent as it suggests that the forces acting upon the spheres are in equilibrium, affirming the observed 7° angle.

To determine the significance of the gravitational force, calculate:

1. The weight (W) of each sphere:
   $W = mg = (3.2 \times 10^{-3} kg)(9.8 \, m/s^2) \approx 0.031 \, N$

2. Comparing to the electrostatic force previously calculated (about 4 × 10^{-3} N),

• W is substantially greater than the electrostatic force.

Thus, the statement that gravitational force has no significant effect is likely incorrect since W considerably exceeds the electrostatic force affecting the angle.