Question

Positive point charge q placed at distance 2r from the surgmface of metallic sphere of radius r the electric potential field at centre is

Answer 1

a positive point charge q is placed at distance 2r from the surface of metallic sphere of radius r.

we have to find electric potential at the centre of sphere.

potential due to metallic sphere at the centre , $V_c$ = potential on the surface of metallic sphere due to metal = 0, [ because induced charge on the surface of metallic sphere due to charge q = 0]

now, potential due to charge q on the surface of metallic sphere, $V_q=\frac{kq}{2r}$

so, net potential at the centre = potential at the surface of metal = $v_c+v_q$ = kq/2r .