Question

Calculate the potential at the centre of a square of side √2 m, which carries charges of 2nC, 1nC, - 2 nC and – 3nC at its four corners.

Answer 1

Given :

The length of side of the square = √2 m

To Find :

The potential at the center of the square

Solution :

• The distance of the center of the square from the four corners is same and equal to half of its length of the diagonal

• By using Pythagoras theorem, Length of the diagonal is

             $x^{2} =(\sqrt{2 } )^{2}+ (\sqrt{2 } )^{2}$

             $x = \sqrt{4}$

             $x = 2m$

• The potential at the center is the algebraic sum of potentials due the the charges present at corners

             $V=k\frac{(q_{1} + q_{2}+ q_{3}+ q_{4})}{r}$

             $V=9\times10^{9}\times\frac{(2-2-3+1)\times10^{-9}}{1}$

             $V=-18\:V$

   The potential at the center of the square is -18 V