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:

  • [JEE MAIN 2021]
  • 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.

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Reason : Electric field at all points on Gaussian surface depends only on charges $q_1$ and $q_2$ .

  • [AIIMS 2012]

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A disk of radius $a / 4$ having a uniformly distributed charge $6 C$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 C$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 C$ and $3 C$ are placed at $(a / 4,-$ $a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x=\pm a / 2, y=\pm a / 2, z=\pm a / 2$. The electric flux through this cubical surface is