Torque on Electric Dipole

Rarely Tested

Torque on Electric Dipole

### Formula

$$\tau=pE\sin\theta$$

### Terminologies

- τ → Torque on dipole.

- p → Dipole moment.

- E → Electric field.

- θ → Angle between p and E.

### Conditions / Special Cases

Maximum torque:

$$\theta=90^\circ$$

$$\tau_{max}=pE$$

No torque:

$$\theta=0^\circ,180^\circ$$

### Usage

- Used in dipole rotation 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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