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Question: The distance between the two charges \(+ q\) and \(- q\) of a dipole is \(r\). On the axial line at ...

The distance between the two charges +q+ q and −q- q of a dipole is rr. On the axial line at a distance dd from the centre of dipole, the intensity is proportional to

A

qd2\frac{q}{d^{2}}

B

qrd2\frac{qr}{d^{2}}

C

qd3\frac{q}{d^{3}}

D

qrd3\frac{qr}{d^{3}}

Answer

qrd3\frac{qr}{d^{3}}

Explanation

Solution

Field along the axis of the dipole

E=14πε0.2pd3=14πε0.2(q×r)d3;E = \frac{1}{4\pi\varepsilon_{0}}.\frac{2p}{d^{3}} = \frac{1}{4\pi\varepsilon_{0}}.\frac{2(q \times r)}{d^{3}}; ∴ E∝qrd3E \propto \frac{qr}{d^{3}}