Question

Three identical charges, each having a value $1.0\times {10}^{-3}C$ are placed at the corners of an equilateral triangle of side 20 cm Find the potential at the center of the triangle

• A. $2.3\times {10}^{6}V$
• B. $2.3\times {10}^{5}V$
• C. $2.3\times {10}^{4}V$
• D. $2.3\times {10}^{3}V$

Answer 1

The correct option is D $2.3\times {10}^{3}V$

$q=1.0\times {10}^{-8}C,t=20cm$

Since it forms an equipotential surface.

So the electric field at the centre is zero.

$\begin{array}{c}r=\frac{2}{3}\sqrt{{\left(2\times {10}^{-1}\right)}^2-{\left({10}^{-1}\right)}^2}\\ =\frac{2}{3}\sqrt{4\times {10}^{-2}-{10}^{-2}}\\ =\frac{2}{3}\sqrt{{10}^{-2}\left(4-1\right)}\\ =\frac{2}{3}\times {10}^{-2}\times 1.732\\ =1.15\times {10}^{-1}\\ V=\frac{3\times 9\times {10}^9\times 1\times {10}^{-8}}{1\times {10}^{-1}}\\ =23\times {10}^2\\ =2.3\times {10}^{3}V\end{array}$