Question

Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius $10\text{cm}$ surrounding the total charge is $25{\text{N-m}}^2/\text{C}$. The flux over a concentric sphere of radius $20\text{cm}$ will be

• A. $25{\text{N-m}}^2/\text{C}$
• B. $50{\text{N-m}}^2/\text{C}$
• C. $75{\text{N-m}}^2/\text{C}$
• D. $100{\text{N-m}}^2/\text{C}$

Answer 1

The correct option is A $25{\text{N-m}}^2/\text{C}$

Electric flux through a spherical surface,
$\Phi =25{\text{N-m}}^2/\text{C}$

Radius of spherical surface, $r=10\text{cm}$

Radius of concentric spherical surface, $R=20\text{cm}$


We know that, electric flux through a spherical surface,

$\varphi =\frac{q}{{\in }_0}$

From the above expression we can say that electric flux is independent of radius.

Therefore, the flux over a concentric sphere of radius $20\text{cm}$ will be equal to flux through spherical surface of radius $10\text{cm}$

$\therefore \varphi =25{\text{N-m}}^2/\text{C}$

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