Question

A hollow metallic sphere of radius 'r' is kept at a potential of 1 volt. The total electric flux coming out of the concentric spherical surface of radius R(>r) is
1. 4πε₀r
2. 4πε0r²
3. 4πε₀R
4. None of the above

Answer 1

Correct Answer - Option 1 : 4πε₀r

Concept:

By Gauss law, \(ϵ \oint \vec{E}.d\vec{s}={{Q}_{encl}}\)

Thus, \(ϵ \oint \vec{E}.d\vec{s}={{ϵ }_{0}}E\left( 4π {{r}^{2}} \right)\)

\(ϕ = \oint \vec{E}.d\vec{s}\)

where ϕ = flux coming out of the concentric sphere.

r = radius of the sphere

Calculation:

Since electric potential can be defined as:

\(V = \frac{Q}{{4πϵ{_0}r}}\)

V = 1 V (given)

Q = 4 π ϵ₀ r

 \(ϕ =ϵ \oint \vec{E}.d\vec{s}={4\pi\epsilon_0r}\)