First slide

Electric dipole

Question

Two electric dipoles each of dipole moment p = 6.2 x 10^-3 C cm are placed with their axis along the same line and their centres at a distance d = 10^-8 m. What is force of attraction between dipoles?

Moderate

A

21 x 10³³N
B

2.1 x 10^-39N
C

21 x 10^-37N
D

2.1 x 10^-17N

Solution

Field at +q due to first dipole = $\frac{1}{4 {πε}_{0}} \frac{2 p}{{(d + l)}^{3}}$
Force on +q due to first dipole = $\frac{1}{4 {πε}_{0}} \frac{2 pq}{{(d + l)}^{3}}$
Force on -q due to first dipole = $\frac{1}{4 {πε}_{0}} \frac{2 pq}{{(d - l)}^{3}}$
Force of interaction = $\frac{2 pq}{4 {πε}_{0}} [\frac{1}{{(d - l)}^{3}} - \frac{1}{{(d + l)}^{3}}]$
$= \frac{3 p^{2}}{2 ε_{0} {πd}^{4}} = 201 x 10^{- 16} N [∵ d > > l]$

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