Question 104 of 311

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 $r\left(\lt R\right)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not
In the light of the above statements, choose the correct answer from the options given below:

ABoth Statement $I$ and Statement $II$ are trueBStatement $I$ is false but Statement $II$ is trueCStatement $I$ is true but Statement $II$ is falseDBoth Statement $I$ and Statement $II$ are false

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Answer: (C) Statement $I$ is true but Statement $II$ is false

$\oint \vec{E}\cdot d\vec{s}=\dfrac{{q}_{in}}{{\epsilon }_{0}}=0=\phi$
Flux of $\vec{E}$ through sphere is zero.
But $\oint \vec{E}\cdot d\vec{s}=0\Rightarrow \left\{\vec{E}\cdot d\vec{s}\neq 0\right\}$ for small section $ds$ only
Statement-$2$

As change encloses within gaussian surface is equal to zero.
$\phi =\oint \vec{E}\cdot d\vec{s}=0$