Question

Given below are two statements:

Statement – I: An electric dipole is placed at the centre of a hollow sphere. The flux of the 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 option given below:

• A. Statement I is true but Statement II is false
• B. Statement I is false but Statement II is true
• C. Both Statement I and Statement II are true
• D. Both Statement I and Statement II are false

Answer 1

The correct option is A

Statement I is true but Statement II is false

Step1: Given data:

Statement-I:

The hollow sphere has an electric dipole at the center.

Statement-II:

The radius of the solid metallic sphere$=R$

The total charge on the solid metallic sphere$=Q$

Step2: Find the flux of the electric field and the electric field for statement-I.

We know that a dipole is a pair of equal and opposite charges separated by a small distance.

$\because$The net charge on the electric dipole, $q_{net}=+q-q=0$

Therefore, according to Gauss's law,

Electric flux, $\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{q_{net}}{{\epsilon }_0}=\frac{0}{{\epsilon }_0}=0$

Where, $\overrightarrow{E}$ is the electric field, $\overrightarrow{ds}$ is the surface area a small section, and ${\epsilon }_0$ is permittivity in free space.

And for a small section $\overrightarrow{ds}$ only, $\overrightarrow{E}.\overrightarrow{ds}\ne 0$

$\therefore$The flux of the electric field throughout the hollow sphere is zero and the electric field is non-zero.

Hence, statement-I is true:

Step3: Find the electric field at any point on the spherical surface of the radius $(r<R)$ and the electric flux passing through this closed spherical surface of the radius $r$ for statement-I.

Since electric field due to charged solid sphere at a distance $r$ from centre when $(r<R)$ as.

$\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}\times \frac{Qr}{R^3}$

$\therefore$The electric field due to the charged solid sphere at a distance $r$ from the centre is non-zero.

As change encloses within the gaussian surface is equal to zero such as.

$\varphi =\oint \overrightarrow{E}.\overrightarrow{ds}=0$

Hence, statement-II is false:

Hence, option A is correct