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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:
Both Statement $I$ and Statement $II$ are true
Statement $I$ is true but Statement $II$ is false
Both Statement $I$ and Statement $II$ are false
Statement $I$ is false but Statement $II$ is true.
Solution
$\oint \vec{E} \cdot \overline{d s}=\frac{q_{i n}}{\varepsilon_{0}}=0=\phi$
Flux of $\overrightarrow{ E }$ through sphere is zero.
But $\oint \overrightarrow{ E } \cdot \overline{ d s}=0 \Rightarrow\{\overrightarrow{ E } \cdot \overline{ d } \neq 0\}$ for small section $ds$
only
Statement$- 2$
As change encloses within gaussian surface is equal to zero.
$\phi=\oint \overrightarrow{ E } \overline{ ds }=0$
