Question

Charges 5c,-2c,3c,-9c are placed at the corners A,B,C and D of a square ABCD of side 1m. The net electric potential at the centre of the square is

Answer 1

Given that,

Charge on A = 5 μC

Charge on B = -2 μC

Charge on C = 3 μC

Charge on D = -9 μC

Side = 1 m

Let the diagonal side OA, OB, OC and OD is x m.

According to figure,

In OAB,

We need to calculate the diagonal distance

Using pythagorean theorem

$AB^2=(OA)^2+(OB)^2$

Put the value into the formula

$1^2=x^2+x^2$

$2x^2=1$

$x=\dfrac{1}{\sqrt{2}}$

All charges are at $\dfrac{1}{\sqrt{2}}\ m$ from center

We need to calculate the net electric potential at the center of the square

Using formula of potential

$V_{net}=\dfrac{kq_{1}}{x}+\dfrac{kq_{2}}{x}+\dfrac{kq_{3}}{x}+\dfrac{kq_{4}}{x}$

$V_{net}=\dfrac{k}{x}(q_{1}+q_{2}+q_{3}+q_{4})$

Put the value into the formula

$V_{net}=\dfrac{9\times10^{9}}{\frac{1}{\sqrt{2}}}(5-2+3-9)\times10^{-6}$

$V_{net}=9\times10^{9}\times\sqrt{2}\times(-3\times10^{-6})$

$V_{net}=-27\sqrt{2}\ kV$

Hence, The net electric potential at the center of the square is $-27\sqrt{2}\ kV$