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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

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B

Statement I is false but Statement II is true

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C

Both Statement I and Statement II are true

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D

Both Statement I and Statement II are false

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Solution

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.

The net charge on the electric dipole, qnet=+q-q=0

Therefore, according to Gauss's law,

Electric flux, E.ds=qnetε0=0ε0=0

Where, E is the electric field, ds is the surface area a small section, and ε0 is permittivity in free space.

And for a small section ds only, E.ds0

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.

E=14πε0×QrR3

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.

ϕ=E.ds=0

Hence, statement-II is false:

Hence, option A is correct


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