An electric dipole with dipole moment

Question:

An electric dipole with dipole moment $4 \times 10^{-9} \mathrm{C} \mathrm{m}$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^{4} \mathrm{~N} \mathrm{C}^{-1}$. Calculate the magnitude of the torque acting on the dipole.

Solution:

Electric dipole moment, $p=4 \times 10^{-9} \mathrm{C} \mathrm{m}$

Angle made by $p$ with a uniform electric field, $\theta=30^{\circ}$

Electric field. $E=5 \times 10^{4} \mathrm{~N} \mathrm{C}^{-1}$

Torque acting on the dipole is given by the relation,

$T=p E \sin \theta$

$=4 \times 10^{-9} \times 5 \times 10^{4} \times \sin 30$

$=20 \times 10^{-5} \times \frac{1}{2}$

$=10^{-4} \mathrm{Nm}$

Therefore, the magnitude of the torque acting on the dipole is $10^{-4} \mathrm{~N} \mathrm{~m}$.

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