Question

Two electric charges one 20 times as strong as the other, exert a force 2.45×10-2 on each other. When they are placed 10 cm apart in air, find the magnitude of each charge.

Answer 1

Explanations & Calculations

• This is quiet straightforward as it's all about applying the Coulomb's equation for the situation.
• $F = \frac{1}{4\pi\epsilon_0}\Big(\frac{q_1q_2}{r^2}\Big) =k\Big(\frac{q_1q_2}{r^2}\Big)$
• k = 9 $\small \times$ 10⁹ Nm²C^-2 in air.

• If the charge of one charge is q then,

$\qquad\qquad \begin{aligned} \small 2.45 \times 10^{-2}N &= \small 9\times10^9\Bigg(\frac{q\times20q}{0.1^2m^2}\Bigg)\\ \small q^2 &= \small 1.3611\times 10^{-15}C^2\\ \small |q| &= \small 3.689\times10^{-8}C \\ &= \small \bold{0.0369\,\mu C}\\ \\ \small |20q| &= \small 20\times 36.89 = \small \bold{0.738 \,\mu C } \end{aligned}$