Two point charges and are placed at a distance of , as shown in the figure. The magnitude of electric field intensity at a distance varies as [2022]

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Solution

Q.
Two point charges $- q$ and $+ q$ are placed at a distance of $L$ , as shown in the figure. The magnitude of electric field intensity at a distance $R (R ≫ L)$ varies as [2022]

1 $\frac{1}{R^{2}}$

2 $\frac{1}{R^{3}}$

3 $\frac{1}{R^{4}}$

4 $\frac{1}{R^{6}}$

Ans.
(2)

Since, $R ≫ L,$ the given charge configuration can be treated as dipole.

Electric field due to a dipole at any arbitrary point $(R, θ)$ is

$E = \frac{p}{4 π ε_{0} R^{3}} \sqrt{3 \cos^{2} θ + 1}$

Here, $E \propto \frac{1}{R^{3}} .$

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