Name: Equipotential Surfaces and Its Properties
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: The surface over which the electric potential is the same everywhere is called an equipotential surface. Let's more about it and its properties in this video.

Question

Derive the formula for the electric potential energy of an electric dipole in a uniform electric field. Discuss its stable and unstable equilibrium state.

Accepted Answer

The potential energy of dipole in a uniform electric field.

$\vec{τ} = \vec{p} \times \vec{E}$

$τ$ is the torque, and $p$ is momentum.

Work done in rotating dipole by small angle

$d w = τ d θ$

$= - p E \sin θ d θ$

The change in potential energy.

$d w = P E \sin θ d θ$

On integrating both the side. We get

$w = \int_{θ_{1}}^{θ_{2}} d w = \int_{θ_{1}}^{θ_{2}} p E \sin θ d θ$

$w = p E [\cos θ_{1} - \cos θ_{2}]$

Now, if $θ_{1} = 0, and θ_{2} = x$

Then, $U = w = p E (1 - \cos x)$ .

The two special cases are as follows

1. When the electric dipole is parallel to the electric field the dipole is in stable equilibrium.

2. When the electric dipole is antiparallel to the electric field, the dipole is in unstable equilibrium.

Derive the formula for the electric potential energy of an electric dipole in a uniform electric field. Discuss its stable and unstable equilibrium state.

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