Question

An electric dipole consists of two opposite charges $\pm q$separated by a small distance s. The product $p=qs$is called the dipole moment. FIGURE P22.60 shows an electric dipole perpendicular to an electric field $\overrightarrow{E}$. Find an expression in terms of p and E for the magnitude of the torque that the electric field exerts on the dipole.

Short answer

$\tau =pE$

Step-by-step solution

Given Information

Separation between the charges $=s$

Electric field strength $=E$

Magnitude of charge $=q$

Dipole moment localid="1648469282144" $=p=qs$

Calculation

Since the given charges are equal and opposite in nature, the corresponding force due to the electric field is equal and opposite.

Hence, the torque at dipole due to each charge will also be equal and will be in the same direction (as per the figure it will be in the anticlockwise direction).

The magnitude of the force on each charge can be given as:

$F=qE$

It is given that the charges are separated by a perpendicular distance $s$

Hence, the total torque can be given as:

$$\begin{gathered} \tau =Fs \\ \tau =qEs \\ \tau =qsE \end{gathered}$$

Since $p=qs$, hence the above equation of torque becomes:

$\tau =pE$

Final answer

Hence, the magnitude of the torque that the electric field exerts on the dipole can be given as:

$\tau =pE$