Question

Which of the following is not true?
 A) For a point charge electrostatic potential varies as $ 1/r $ .
 B) For a dipole potential depends on position vector and dipole moment vector.
C) The electric dipole potential varies $ 1/r $ at a large distance.
D) For a point charge electrostatic field varies as $ 1/{r^2} $

Answer 1

Hint : A dipole is a pair of oppositely charged particles that are placed a certain distance apart. Dipoles are used to describe the interactions between molecules where the separation distances between atoms of the molecules are very close compared to the distances between two molecules.

Complete step by step answer
The electrostatic potential of a point charge is a function of the distance of the point from the point charge. It can be calculated as $ V = \dfrac{{kq}}{r} $ .The relation is inverse and can be written as $ V \propto 1/r $ . So, option (A) is true.
For a dipole potential, the electric potential is calculated as:
 $ V = \dfrac{{k\hat p.\hat r}}{{{r^2}}} $ where $ \hat p $ is the dipole moment unit vector and $ \hat r $ is the unit vector of the position of the point at which we want to calculate the potential. So, option (B) is also true. Here $ \hat r $ is a unit vector and only denotes direction. The potential due to a dipole at any point also depends on the position of the point at which we are measuring the electric potential with respect to the axis of the dipole.
As discussed above, we can see that the electric dipole moment $ V \propto \dfrac{1}{{{r^2}}} $ so option (C) is incorrect. Hence it is the correct choice since we’ve been asked to find the false statement.

Note
The electrostatic field for a point charge is different than the field of a dipole and is calculated as $ E = \dfrac{{kQ}}{{{r^2}}} $ so option (D) is also correct. Electric dipoles and point charges have different dependences of electric fields and potentials on the distance of the charges so we must be careful not to confuse them with each other.