Potential Energy of Electric Dipole in Uniform Electric Field

Rarely Tested

Potential Energy of Electric Dipole in Uniform Electric Field

### Formula

$$U=-pE\cos\theta$$

### Terminologies

- U β†’ Potential energy of dipole.

- p β†’ Electric dipole moment.

- E β†’ External electric field.

- ΞΈ β†’ Angle between dipole moment and electric field.

### Conditions / Special Cases

For stable equilibrium:

$$\theta=0^\circ$$

$$U_{min}=-pE$$

For unstable equilibrium:

$$\theta=180^\circ$$

$$U_{max}=pE$$

### Usage

- Used in dipole energy and orientation problems.

Question 1

Consider an electric dipole comprising two charges $$+q$$ and $$-q$$ each with mass $$m$$, separated by a fixed distance $$d$$ and initially at rest with its dipole moment pointing along $$\hat{i}$$. A uniform electric field $$E\hat{j}$$ is turned on at time $$t=0$$ and it is turned off at $$t=t_f$$, when the dipole moment makes an angle $$\theta_f$$ with $$\hat{i}$$. Neglecting any sources of energy loss, correct option(s) is/are:

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