An electric dipole $\vec{P}=2qa\,\hat{i}$ is placed in the x-y plan...

Question

An electric dipole $\vec{P}=2qa\,\hat{i}$ is placed in the x-y plane, centred at the origin. Let $E_1$ and $E_2$ be the magnitudes of the electric field at a point distant $r\,(\gg a)$ from its centre, along its axis and on its equatorial plane respectively. Then the value of $\left(\dfrac{E_1}{E_2}\right)$ is:

Accepted Answer

Electric field on the axial line of a dipole: $$E_1 = \frac{1}{4\pi\varepsilon_0}\frac{2p}{r^3}$$ Electric field on the equatorial line of a dipole: $$E_2 = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^3}$$ Taking the ratio: $$\frac{E_1}{E_2} = \frac{2p/r^3}{p/r^3} = 2$$ Hence the correct option is (C).

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