Question

Which of the following is not true?

• A. At large distances, the electric dipole potential varies as $\frac{1}{r}$
• B. Electrostatic potential varies as $\frac{1}{r}$for a point charge
• C. The potential depends on the magnitude of position vector and dipole moment vector for a dipole.
• D. The electrostatic field varies as $\frac{1}{r^2}$for a point charge

Answer 1

The correct option is A

At large distances, the electric dipole potential varies as $\frac{1}{r}$

Explanation of correct option:

In the case of option (A),

At a large distance ‘r’ from the center of the dipole, the potential is given by, $V=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{p\cos \theta }{r^2}$

Here, $p$=dipole moment

${\epsilon }_0$ = permittivity of free space

$\theta$ = angle between displacement vector and dipole moment

Therefore, $V$∝$\frac{1}{r^2}$, and the assertion in option(A) is incorrect.

Explanation of incorrect options:

In the case of option (B),

Electric potential due to a point charge is given by, $V=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{q}{r}$, where $q$is the magnitude of charge.

Therefore, $V$∝$\frac{1}{r}$and the assertion in option (B) stands correct.

In the case of options (C),

At a large distance ‘r’ from the center of the dipole, the potential of the dipole is given by, $V=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{p\cos \theta }{r^2}$

Therefore, the assertion in option (C) stands correct.

In the case of option (D),

Electric field due to a point charge is given by, $E=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{q}{r^2}$

Therefore, $E$∝$\frac{1}{r^2}$and the assertion in option (D) stands correct.

Hence, option (A) is the correct answer.