Dipole Potential Energy
Potential energy of dipole is the energy possessed by the dipole by virtue of its particular position in the electric field.
Suppose an electric dipole of moment ~P is oriented at a ∠ θ with the direction of uniform external electric field ~E. We know that, the torque ~ζ acting on the dipole is
ζ = p E sin θ
It tries to rotate the dipole.
Small amount of work done in rotating the dipole through a small angle d θ against the torque is
dW = ζ d θ
= p E sin θ d θ
∴ Total work done in rotating the dipole from orientation θ1 to θ2 is
W =θ1∫θ2 E sin θ d θ
= p E [- cos θ]θ1θ2
W = - p E [cos θ2 – cos θ1] (1)
P.E. = W = - pE (cos θ2 – cos θ1) (2)
When the dipole is initially aligned along the electric field i.e. θ1 = 0°, and we have to set it angle θ with ~Ei.e. θ2 = θ.
From (2), W = - pE (cos θ – cos 0°)
W = - pE (cos θ – 1) (3)
This work done is stored in the dipole in the form of potential energy.
When the dipole is initially at right angle to ~E i.e. θ1 = 90°, and we have to set it at angle θ with ~E i.e.θ2 = θ.
∴ From (2), W = - pE (cos θ – cos 90°)
W = - pE cos θ
∴ Potential energy of dipole,
U = W = - pE cos θ (4)
U = - ~P.~E (5)
Obviously, potential energy of an electric dipole is a scalar quantity. It is measured in joule.
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