Question

Three identical spheres each having a charge $q$ and radius $R$ are kept in such a way that each touches the other two spheres. The magnitude of electric force on any sphere due to the other two is equal to

• A. $\frac{R}{2}\frac{1}{4\pi ϵ}\frac{\sqrt{5}}{4}(\frac{q}{R}{)}^2$
• B. $\frac{1}{2}\frac{1}{4\pi ϵ}\frac{\sqrt{2}}{3}(\frac{q}{R}{)}^2$
• C. $\frac{1}{4\pi ϵ}\frac{\sqrt{3}}{4}(\frac{q}{R}{)}^2$
• D. $\frac{-1}{2}\frac{1}{4\pi ϵ}\frac{\sqrt{3}}{\sqrt{2}}(\frac{q}{R}{)}^2$

Answer 1

The correct option is C $\frac{1}{4\pi ϵ}\frac{\sqrt{3}}{4}(\frac{q}{R}{)}^2$

$F_{net}=\frac{K{q}^2}{{\left(2R\right)}^2}.2\cos \theta \frac{K{q}^2}{{4R}^2}.2\frac{R\sqrt{3}}{2R}\frac{\sqrt{3}K{q}^2}{{4R}^2}\frac{1}{4\pi {\epsilon }_0}\frac{\sqrt{3}}{4}{\left(\frac{q}{R}\right)}^2$