Question

Four charges each of charges 5 micro-coulomb are placed at the four corners of side 10cm. What is the electrical potential at the centre of square
1.) 4500V
2.) 4500√2V
3.) 4500/√2V
4.) Zero

Answer 1

Given info : Four charges each of charges 5 micro-coulomb are placed at the four corners of side 10m.

To find : the electrical potential due to each charge at the centre of square is ...

solution : we know centre of square is the midpoint of diagonal of square.

so, distance of centre to a vertex of square , r = d/2 =√2a/2 = a/√2 , [ we know, diagonal of square , d = √2a , a is side length of square. ]

here, a = 10 cm ⇒ r = 10/√2 = 5√2 m

now electrical potential due to each charge at the centre of square, V = $\frac{kq}{r}$

=$\frac{9\times10^9\times5\times10^{-6}}{5\sqrt{2}}$ = $\frac{9}{\sqrt{2}}\times10^3$ = $4500\sqrt{2}$ volts

therefore the electric potential due to each charge at the centre of the square is $4500\sqrt{2}$ volts. hence option (2) is correct choice.