Question

$1\mu \text{C}$ charge is uniformly distributed on a spherical shell given by equation $x^2+y^2+z^2=25$. What will be the flux through an imaginary sphere of radius $3\text{m}$ and centre at origin ?

• A. $5{\text{N-m}}^2/\text{C}$
• B. $25{\text{N-m}}^2/\text{C}$
• C. $50{\text{N-m}}^2/\text{C}$
• D. Zero

Answer 1

The correct option is D Zero

Given:
Charge, $q=1\mu \text{C}={10}^{-6}\text{C}.$

Equation of spherical shell,
$x^2+y^2+z^2=25$
that means, centre of spherical shell is origin and radius, $R=5\text{m}$.

Radius of imaginary sphere, $r=3\text{m}$


Here, $R>r$

As there is no charge inside the imaginary sphere, i.e. $q=0$.

So, electric flux $\varphi$ through imaginary sphere is given by

$\varphi =\frac{q}{{ϵ}_0}=0$

So, option $\left(d\right)$ is correct.