Q.

Derive an expression for the potential energy of an electric dipole placed in a uniform electric field?

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answer is 1.

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Detailed Solution

Consider an electric dipole placed in a uniform electric field E with its dipole moment P makes an angle θ with field. Two forces on two charges creates couple will be

τ=qE×2asinθ=PEsinθ

If the dipole is rotated through a small angle dθ against the torque acting on it, then small work done is w=τdθ
dw=PEsinθdθ
The total work done in rotating the dipole from angle θ1 to θ2 with the direction of field
w=dw=θ1θ2PEsinθdθ=PEθ1θ2sinθdθ=PE[cosθ]θ1θ2
w=PEcosθ1cosθ2
This work done is stored as potential energy of dipole
u=PEcosθ1cosθ2

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