Question

Two identical charges are 30 cm apart and experience a force of 0.85 N. Find the charge on each sphere.

Answer 1

We are given the following information

Two charges are identical = q1 = q2 = q

Distance between charges = r = 30 cm = 30/100 = 0.30 m

Force experienced by charges = F = 0.85 N

We are asked to find the charge on each sphere.

Recall that Coulomb’s law is given by

`F=k(q_1q_2)/(r^2)`

Where k is the Coulomb constant that is k = 9x10⁹ Nm²/C²

Since the two charges are identical, q1 = q2 = q

`\begin{gathered} F=k(q^2)/(r^2) \\ q^2=(F\cdot r^2)/(k) \\ q^2=(0.85\cdot0.30^2)/(9*10^9) \\ q^2=8.5*10^(-12) \\ q=\sqrt{8.5*10^(-12)} \\ q=2.915*10^(-6)\; C \end{gathered}`

Therefore, the charge on each sphere is 2.915×10⁻⁶ C