Question

If one penetrates a uniformly charged spherical cloud, electric field strength

• A. decreases directly as the distance from the centre
• B. increases directly as the distance from the centre
• C. remains constant
• D. None of these

Answer 1

Answer: (A)

decreases directly as the distance from the centre

The charge on the spherical cloud be $Q$ having charge density $\rho$

Let a Gaussian sphere of radius $r$ which contains charge $q$

$\therefore$ $q=\frac{4\pi }{3}{r}^3\times \rho$

Now let the electric field at circumference of Gaussian sphere be $E$

Using Gauss's law : $\oint \overrightarrow{E}.\overrightarrow{da}=\frac{q_{enclosed}}{{ϵ}_o}$

$E\left(4\pi r^2\right)=\frac{\frac{4}{3}\pi r^3\rho }{{ϵ}_o}$ $⟹E_r=\frac{\rho r}{3{ϵ}_o}$

Hence $E_r$ decreases directly as the distance from the center $\left(r\right)$ decreases.