Question

Calculate electric filed intensities on charging a spherical conductor of radius $R$ with charge $q$ in following consitions:
(a)$r>R$
(b) $r<R$
(c) on the spherical surface
(d) at the centre of sphere
Plot a graph electric field intensity and distance.

Answer 1

Electric field intensity due to uniformly charged conducting sphere 'the charge given to a conductor always rests on its surface Therefore charge given to a spherical conductor will rest on its surface ; hence the charged spherical conductor will behave as spherical shell. Therefore the expressions for electric field will same as those for spherical shell i.e.

(i) Intensity of electric field outside the sphere at distance r from its centre

$E_0=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}=\frac{\sigma }{{ϵ}_0}\frac{R^2}{r^2}$

(ii) Intensity of electric field at the surface of the sphere

$E_S=\frac{1}{4\pi {ϵ}_0}\frac{q}{R^2}$

(iii) Inside the charged sphere ,

$E_{in}=0$