Question

Three identical charges, each having a value $1.0\times {10}^{-8}C$, are placed at the corners of an equilateral triangle of side $20cm$. Find the electric field and potential at the centre of the triangle.

Answer 1

$d=\frac{2}{3}\left(\frac{\sqrt{3}}{2}a\right)$

$=\frac{a}{\sqrt{3}}$

$V=3\times \frac{1}{4\pi {ϵ}_0}\times \frac{q}{d}=\frac{3\times 9\times {10}^9\times \left({10}^{-8}\right)\left(\sqrt{3}\right)}{(2\times {10}^{-1})}$

$=\frac{27\sqrt{3}}{2}\times {10}^2$

$x=a\sin 60=\frac{\sqrt{3}a}{2}$

$d=\frac{2}{3}\left(x\right)=\frac{a}{\sqrt{3}}$.