Question

17. Four charges each of 5 mu C are placed at the four corners of a square of side 10 cm. What is the electric potential at the centre of square? (a) 4500 V (b) 4500 sqrt 2 1 ( 5) 4500 sqrt 2 (d) Zero​

Answer 1

Given info : Four charges each of 5μC are placed at the four corners of a square of side 10cm.

To find : the electric potential at the centre of square is ..

solution : centre of a square is the midpoint of a diagonal of it.

so, the distance between a vertex to the centre of square , a = $\frac{\text{diagonal}}{2}$

= $\frac{\sqrt{2}\times\text{side of square}}{2}$

= 5√2 cm

now electric potential at the centre of square due to each vertex of it is given by, V = $\frac{kQ}{a}$

where, k = 9 × 10⁹ Nm²/C² , Q = 5 × 10⁻⁶ C and a = 5√2 × 10⁻² m

now, V = $\frac{9\times10^9\times5\times10^{-6}}{5\sqrt{2}}$ volts = $4500\sqrt{2}\text{volts}$

see diagram,

   electric potential due to charge placed at A is cancelled by electric potential due to charge placed at C.

similarly, electric potential due to charge placed at B is cancelled by electric potential due to charge placed at D.

so, net electric potential = $(4500\sqrt{2}-4500\sqrt{2})+(4500\sqrt{2}-4500\sqrt{2})$ = 0 volts

Therefore the electric potential at the centre of square is zero. option (d) is correct choice.