Derive an expression for potential energy of electric-di-pole placed in an uniform electric field.

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Accepted Answer

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> [!TLDR]
> The potential energy of a dipole in a uniform field is $U = -pE\cos	heta = -\vec{p}\cdot\vec{E}$, derived from the work done against the aligning torque.
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> **Concept.** A dipole of moment $p$ in a uniform field $E$ experiences a torque $	au = pE\sin	heta$ that tends to align it with the field. Rotating the dipole against this torque stores potential energy.
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> **Derivation.** The work done in rotating the dipole through a small angle $d	heta$ against the torque is
> $$dW = 	au\, d	heta = pE\sin	heta\, d	heta.$$
> Taking the reference position at $	heta_0 = 90^\circ$ (where $U = 0$), the potential energy at angle $	heta$ is …

Q.Derive an expression for potential energy of electric-di-pole placed in an uniform electric field.

Concept understanding — Electric Dipole in a Field

Electric Dipole in a Uniform Field — First Look

What happens? Two forces, one twist

The torque formula

What does this mean physically?

Q.Derive an expression for potential energy of electric-di-pole placed in an uniform electric field.

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