Question

Two electrically neutral spheres are separated by 1.0 cm. Electrons are removed from one sphere and transferred to the other until a force of magnitude 1.0 × 10−6 N is generated between the two spheres. How many electrons were transferred in the process? Choose the correct answer.

Answer 1

We will note the number of electrons transferred by $N$ . After the transfer first sphere is charged with a charge $N |e|$ and second is charged with $-N|e|$ , where $e$ denotes a charge of an electron. Therefore a force between two spheres is equal to :

$F = \frac{1}{4\pi \varepsilon_0} \frac{Q_1 Q_2}{r^2} = \frac{1}{4\pi \varepsilon_0} \frac{-N^2 e^2}{r^2}$ , where $r$ is a distance between two spheres.

Thus we have

$N^2 = \frac{4\pi\varepsilon_0 |F| r^2}{e^2}$

$N = \frac{2r}{e} \sqrt{\pi \varepsilon_0|F|} = \frac{2\cdot10^{-2}}{1.6\cdot10^{-19}}\sqrt{\pi\cdot8.85\cdot10^{-12}\cdot10^{-6}}$

$N\approx 6.6\cdot 10^8$