First slide

Electrostatic force

Question

Three identical spheres each having a charge 2q and radius R are kept such that each touches the other two. Find the magnitude of the electric force on any sphere due to the other two

Moderate

A

$\frac{3 q^{2}}{4 {πε}_{0} R^{2}}$
B

$\frac{\sqrt{3} q^{2}}{2 {πε}_{0} R^{2}}$
C

$\frac{\sqrt{3} q^{2}}{8 {πε}_{0} R^{2}}$
D

$\frac{\sqrt{3} q^{2}}{4 {πε}_{0} R^{2}}$

Solution

$\begin{array}{l} F = \frac{1}{4 {πε}_{0}} \frac{(2 q)^{2}}{(2 R)^{2}} = \frac{q^{2}}{4 {πε}_{0} R^{2}} \\ F_{net} = \sqrt{F^{2} + F^{2} + 2 F^{2} \cos 60^{0}} \\ \Rightarrow F_{net} = \sqrt{3} F = \sqrt{3} \frac{q^{2}}{4 {πε}_{0} R^{2}} \\ \Rightarrow F_{net} = \sqrt{3} \frac{q^{2}}{4 {πε}_{0} R^{2}} \end{array}$

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