CBSE Class 12 · 2013 · ElectrostaticsLong Answer

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(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Solution

(a) Dipole moment

p = q (2 a)

is a vector directed from

- q

+ q

.
Let P be an equatorial point at distance

r

from the centre O; each charge is at

r^{2} + a^{2}

E_{+} = E_{-} = \frac{1}{4 π ε _{0}} \frac{q}{r ^{2} + a ^{2}}

The perpendicular components cancel; the axial components add, with

cos θ = \frac{a}{r ^{2} + a ^{2}}

E = 2 E_{+} cos θ = \frac{1}{4 π ε _{0}} \frac{p}{( r ^{2} + a ^{2} ) ^{3/2}}

directed anti-parallel to

p

. For

r ≫ a

E = \frac{1}{4 π ε _{0}} \frac{p}{r ^{3}}

(b) The equipotentials are symmetric about the axis; the potential is zero everywhere on the equatorial plane, since each point there is equidistant from

+ q

and

- q

CBSE Class 12 Board · 2013 · Subjective

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CBSE Class 12 · 2013 · ElectrostaticsLong Answer

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