Question

The force acting on a point charge due to an electric dipole depends upon:
(a) \[F \propto \dfrac{1}{r}\]
(b) \[F \propto \dfrac{1}{{{2^2}}}\]
(c) \[F \propto \dfrac{1}{{{r^3}}}\]
(d) \[F \propto \dfrac{1}{{{r^4}}}\]

Answer 1

Hint: We are asked to find the relation between the force acting on a point charge due to a dipole and the its relation with the dipole. We can start by writing down the formula for the electric field due to an electric dipole and use the relation between electric field and electric force and establish a relation between electric force and distance to find our solution.

Formulas used:
1. The electric field due to an electric dipole is given by the formula,
\[E \propto \dfrac{1}{{{r^3}}}\]
We use this formula as there are two ways of finding the electric field due to an electric dipole. They are along the axis of the electric dipole and perpendicular to it. to the dipole. In either of the cases the end result of proportionality is the same.

2. The relation between electric field and electric force is given by the formula,
\[F = Eq\]
Where \[q\] is the charge

Complete answer:
Let us start by writing down the relation between electric field due to an electric dipole. Which is given by,
\[E \propto \dfrac{1}{{{r^3}}}\]

Now the relation between electric field and electric force is to be noted and it is given by,
\[F = Eq\]

From the two equations above we can conclude that,
\[\dfrac{F}{q} \propto \dfrac{1}{{{r^3}}}\]

Since the charge is also a constant in an electric dipole, we can rewrite the above equation as follows,
\[F \propto \dfrac{1}{{{r^3}}}\]

Which implies that the correct answer is option (c) \[F \propto \dfrac{1}{{{r^3}}}\].

Note: An electric dipole is an arrangement of two charges of equal but opposite magnitudes separated by a distance. An example of an electric dipole is shown below where ‘q’ is the charge.