Question

Charge Q is distributed on a metallic sphere of radius a. What is the electric field at a point a distance r from the center of the sphere? Consider both cases r > a and r < a.

Answer 1

Answer:

a)E= 0  

b) $E=\dfrac{Q}{\varepsilon _o\times 4\pi a^2}\ N/C$

Explanation:

Given that

Charge Q is distributed on a metallic sphere of radius a

a)r < a.

At a radius r ,from gauss theorem

$E.ds=\dfrac{q_i}{\varepsilon _o}$

But in the sphere there is no any charge inside the sphere so

$E.ds=\dfrac{o}{\varepsilon _o}$

E.ds = 0

E= 0

b) r > a

At a radius r ,from gauss theorem

$E.ds=\dfrac{q_i}{\varepsilon _o}$

$E\times 4\pi a^2=\dfrac{Q}{\varepsilon _o}$

$E=\dfrac{Q}{\varepsilon _o\times 4\pi a^2}\ N/C$