Question

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

Answer 1

Hint: For a pair of opposite magnitude q charges, a dipole moment is defined in the magnitude of the charge times the distance to the positive charge between them and the defined direction. It is a good idea in atoms and molecules, where the charging separation effects can be calculated, but the charging distances are too short to be easily detectable. In dielectric and other uses in rigid and fluid materials it is also a valuable term.

Complete step by step solution:
As a function of the point charge the electrostatic potential varies inversely proportional to the charge distance. It can be represented as \[V \propto \dfrac{1}{r}\]
The dipole’s potential depends on the scale of the vector of the position and the vector of the dipole. This can be given by $V = \dfrac{{\hat p.\hat r}} {{4\pi {\varepsilon _0} {r^2}}} $
The electrical potential is a scalar field with a gradient that becomes the vector field. Due to the fact that it is a scalar field, a charging device makes it easier to find potential. It is the summation of electrical potentials by single charges at some points.

The amount of work required to transfer a unit positive charge from a point of reference to a certain point within an electric field without generating acceleration is an electric potential. A dipole is a pair of opposite charges with identical lengths $d$.
The electric charge is given by $F = \dfrac{e}{{4\pi {\varepsilon _0} {r^2}}} $ . This shows that the electric field is inversely proportional to $\dfrac {1} {{{r^2}}} $.

Therefore, the answer is option (C).

Note: The electrical potential is a scalar field with a gradient that becomes the vector field. Due to the fact that it is a scalar field, a charging device makes it easier to find potential. It is the summation of electrical potentials by single charges at some points.