The electric field due to a short electric dipole at a large distance r from the center of the dipole on the equatorial

Question

The electric field due to a short electric dipole at a large distance r from the center of the dipole on the equatorial plane varies with distance as

Accepted Answer

Given: A short electric dipole and a point at a large distance $r$ on the equatorial plane.

Find: How the electric field varies with distance $r$ .

Recall the electric field expression for a short dipole on the equatorial plane:

E = \frac{1}{4\pi\varepsilon_0}\,\frac{p}{r^3}

where $p$ is the dipole moment.

From this expression, the distance dependence is

E \propto \frac{1}{r^3}

Therefore, the electric field varies inversely as the cube of the distance. The correct option is C.

Given: The field of a short electric dipole is to be compared by its dependence on $r$ .

Find: The power of $r$ in the denominator on the equatorial plane.

For a short dipole, both axial and equatorial fields fall off as

\frac{1}{r^3}

Only the numerical coefficient changes between the two cases.

Therefore, the correct variation is $1/r^3$ , so the correct option is C.

Answer