Two charges of each magnitude $$0.01$$ C and separated by a distance of $$0.4$$ mm constitute an electric dipole. If the dipole is placed in an uniform electric field $$\vec{E}$$ of $$10$$ dyne $$\cdot$$ C$$^{-1}$$ making $$30°$$ angle with $$\vec{E}$$, the magnitude of torque acting on dipole is:

The torque on an electric dipole in a uniform electric field is given by:

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

where $$p = qd$$ is the dipole moment.

Given: $$q = 0.01$$ C, $$d = 0.4$$ mm $$= 0.4 \times 10^{-3}$$ m, $$\theta = 30°$$

Convert electric field: $$E = 10$$ dyne/C. Since $$1$$ dyne $$= 10^{-5}$$ N:

$$E = 10 \times 10^{-5} = 10^{-4} \text{ N/C}$$

Dipole moment:

$$p = qd = 0.01 \times 0.4 \times 10^{-3} = 4 \times 10^{-6} \text{ C·m}$$

Torque:

$$\tau = pE\sin\theta = 4 \times 10^{-6} \times 10^{-4} \times \sin 30°$$

$$\tau = 4 \times 10^{-10} \times 0.5 = 2.0 \times 10^{-10} \text{ N·m}$$

The magnitude of torque is $$\mathbf{2.0 \times 10^{-10}}$$ N m.