Question

Which of the following is not true?

• A. For a point charge, electrostatic potential varies as 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 1/r at a large distance
• D. For a point charge, the electrostatic field varies as 1/r².

Answer 1

The correct option is C

The electric dipole potential varies as 1/r at a large distance

Explanation for correct option:

In the case of option C,

1. A dipole is defined as a pair of opposite charges with d the distance between them.
2. The electrical potential is a gradient scalar field that becomes a vector field.
3. A charging device makes it easier to find potential because it is a scalar field. In some locations, it is the summation of electrical potentials by single charges.
4. For an Electric dipole, we have,
   • $V=\frac{1}{4\pi {\epsilon }_o}\left(\frac{q}{r^2}\right)\Rightarrow V\propto \frac{1}{r^2}$
   • Where $V$ is the electric dipole potential, ${\epsilon }_o$ is the permeability of space, $q$ is the charge, and $r$ is the distance between charges.
5. Electric dipole potential varies inversely with the square of the distance.
6. Hence, the electric dipole potential does not vary as $\frac{1}{r}$ at a large distance, It varies as $\frac{1}{r^2}$

Explanation for incorrect option:

In the case of option A:

1. An electric potential is the amount of work necessary to move a unit positive charge from a point of reference to a specific point within an electric field without causing acceleration.
2. The electrostatic potential varies inversely proportionate to the charge distance
3. It is written as, $V\alpha \frac{1}{r}$
   1. Where $V$ is electrostatic potential and $r$ is the distance between charge.
4. Hence, for a point charge, electrostatic potential varies as 1/r.
5. So option A is incorrect.

In the case of option B:

1. The dipole's potential is determined by the scale of the position vector and the dipole's vector.
2. It can be given by, $V=\frac{p^.r^}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}{\mathrm{r}}^2}$
3. Hence, for a dipole, the potential depends on the magnitude of the position vector and dipole moment vector.
4. So option B is not correct.

In the case of option D:

1. When charge carriers, such as electrons, are stationary, electrostatic fields can form as a result of a potential difference or voltage gradient.
2. Electric charge is given by, $F=\frac{e}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}{\mathrm{r}}^2}$
   1. Where $e$is a charge, ${\epsilon }_o$is the permeability of space, and is the distance between charges.
3. This shows that the electric field is inversely proportional to the square of the distance between charges.
4. Hence, The electrostatic field varies as $\frac{1}{r^2}$ for a point charge.
5. So option D is not correct.

Hence option C is correct.