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)

$\oint \vec{ E } \cdot \overrightarrow{ ds }=\frac{ q _{ in }}{\varepsilon_{0}}=0=\phi$
Flux of $\vec{ E }$ through sphere is zero.
But $\oint \vec{ E } \cdot \overrightarrow{ ds }=0 \Rightarrow \{\vec{ E } \cdot \overrightarrow{ ds } \neq 0\}$ for small section $ds$
only
Statement- 2

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