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 the 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 any 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. Both Statement $I$ and Statement $II$ are true
• B. Statement $I$ is true but Statement $II$ is false
• C. Both Statement $I$ and Statement $II$ are false
• D. Statement $I$ is false but Statement $II$ is true.

Answer 1

Answer: (B)

$\oint \vec{E}\cdot \overrightarrow{ds}=\frac{q_{in}}{{\epsilon }_0}=0=\varphi$
Flux of $\vec{E}$ through sphere is zero.
But $\oint \vec{E}\cdot \overrightarrow{ds}=0\Rightarrow \{\vec{E}\cdot \overrightarrow{ds}\ne 0\}$ for small section $ds$
only
Statement- 2

As change encloses within gaussian surface is equal to zero.
$\varphi =\oint \vec{E}\cdot \overrightarrow{ds}=0$
Option(2) statement- 1 correct statement- 2 false.