Question

An electric dipole is placed at the center of an imaginary sphere. Which of the following option is/are correct?

• A. The electric field is zero at every point of the sphere
• B. The flux of the electric field at every point of the sphere is zero
• C. The electric potential is zero at every point of the sphere
• D. The electric potential is zero on a circle on the surface

Answer 1

Answer: (B), (D)

The electric potential is zero on a circle on the surface

Gauss's law of electric flux

1. The total electric flux that passes through a closed surface is equal to the total charge inside in, divided by the permittivity of that medium.
2. Gauss's law is defined by the form, $\int \overrightarrow{E}.\overrightarrow{ds}=\frac{Q}{{\epsilon }_o}$, where, E is the electric flux, ds is the small surface and Q is the total charge inside the surface, ${\epsilon }_o$ is the permittivity of free space.

Explanation for the correct options

Option (B)

1. We know that a dipole consists of two equal and opposite charges. So, the net charge of the dipole placed on the sphere is zero.
2. According to Gauss's law, the electric flux through the sphere is, $\oint \overrightarrow{E}.\overrightarrow{ds}=0$, since the net charge in the sphere is zero.
3. So, the electric flux at every point of the sphere is zero.

Option (D)

1. Potential in a point due to a charge $q$ is $\frac{q}{r}$, where r is the distance of the point from the charge $q$. It is important that for a positive charge, the potential is positive and for a negative charge, it is negative.
2. The electric potential in the middle of the dipole is zero. If we visualize this, then we will get a circle containing all middle points, where the electric potential is zero.

Explanation for the incorrect options

Option (C)

1. The electric potential due to the dipole in the every point of the sphere is not zero.
2. As we know, potential is $\frac{q}{r}$, it is depends on the distance from the point to charge, where potential have to be find.
3. The dipole is not uniform with respect to the sphere, so electric potential can't be zero in this case.

Option (A)

1. Electric field is inversely proportional to the distance of the point (where electric field have to be find) from the charge.
2. The dipole is not uniform with respect to the sphere, so electric field can't be zero in this case.

So, option (B) and option (D) is correct.