Question

Given below are two statements.

Statement $I$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but electric field is not zero anywhere in the sphere.

Statement $II$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at a point on the spherical surface of radius $r(<R)$ is zero, but the electric flux passing through this closed spherical surface of radius $r$ is not zero.

In the light of the above statements, choose the correct answer from the options given below.

• A. Statement $I$ is true, but statement $II$ is false.
• B. Statement $I$ is false, but statement $II$ is true.
• C. Both statement $I$ and statement $II$ are true.
• D. Both statement $I$ and statement $II$ are false.

Answer 1

The correct option is A Statement $I$ is true, but statement $II$ is false.

We know that, electric flux,
$\varphi =\frac{q_{\text{enclosed}}}{{ϵ}_o}$

As $q_{\text{enclosed}}=q+(-q)=0\Rightarrow \varphi =0$

But, $E_{\text{inside}}\ne 0$ as there is net field due to both charges.

So, statement $1$ is true.

Also, for a conducting sphere of radius $R$, all the charges reside on its surface.

Therefore, the electric flux passing through the closed spherical surface of radius $r(<R)$ is zero as $q_{\text{enclosed}}=0$.

And, the electric field inside the conductor is zero.

So, statement $2$ is false.