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Q.

A small electric dipole is of dipole moment p. The electric potential at a distance ‘r’ from its centre and making an angle $θ$ from the axis of dipole will be:

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a

$\frac{kpsinθ}{r^{2}}$

b

$\frac{kpcosθ}{r^{2}}$

c

$\frac{kp}{r^{3}} \sqrt{1 + 3 \sin^{2} θ}$

d

$\frac{kp}{r^{3}} \sqrt{1 + 3 \cos^{2} θ}$

answer is B.

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Detailed Solution

Question Image

Potential at D $V_{D} = \frac{kq}{BD} - \frac{kq}{AD}$

$BD = r - acosθ, AD = r + acosθ$

$V_{D} = \frac{kq}{r - acosθ} - \frac{kq}{r + acosθ}$

$use (r >> acosθ, & P = q \cdot 2 a)$

$\Rightarrow V_{D} = \frac{kq (2 acosθ)}{r^{2}} = \frac{kpcosθ}{r^{2}}$

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A small electric dipole is of dipole moment p. The electric potential at a distance ‘r’ from its centre and making an angle θ from the axis of dipole will be: