A given charge situated at a distance r from an electric dipole on its axis experience a force f. If the distance of the charge from the dipole is doubled, the force acting on the charge will be

Question

Question

This question was previously asked in

RPSC 2nd Grade Science - 2015 Official Paper

Answer 1

Concept:

The magnitude of the electric force experienced by a charge q, placed at a distance r from the dipole will be

⇒ F = qE

The electric field E due to dipole on its axis is given by:

\(E=k\frac{2p}{r^3}\)

∴ \(F=k\frac{2pq}{r^3}\)

or \(F \propto\frac{1}{r^3}\)

Calculation:

Given:

F₁ = f, r₁ = r, r₂ = 2r

\(F \propto\frac{1}{r^3}\)

\(\frac{F_2}{F_1} =\frac{r_1^3}{r_2^3}\)

\(\frac{F_2}{f} =\left(\frac{r}{2r}\right)^3\)

\({F_2} =\frac{f}{8}\)