(Determining unknown charges from force measurements) Two small identical spheres and

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

(Determining unknown charges from force measurements) Two small identical spheres

P

and

Q

, carrying unknown charges

q_1

and

q_2

, are placed

0.20\,\text{m}

apart in air. The electrostatic force between them is found to be

0.20\,\text{N}

and is repulsive. The spheres are now brought into contact, allowed to share charge, and then separated to a distance of

0.30\,\text{m}

. The force is again measured and is

0.10\,\text{N}

, still repulsive. Take

k = 9.0\times10^{9}\,\text{N m}^2\text{C}^{-2}

. (i) Express the first force measurement in terms of

q_1

and

q_2

. (ii) After contact, show that each sphere carries charge

q = \dfrac{q_1+q_2}{2}

, and use the second force measurement to evaluate

q

numerically. (iii) Hence obtain the initial charges

q_1

and

q_2

, stating their magnitudes and signs, and verify that the algebraic sum of charge is the same before and after contact.