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

Given two charges each of magnitude $0.01 \,\text{C}$ and separated by a distance of $0.4 \,\text{mm} = 0.4 \times 10^{-3} \,\text{m}$, we can calculate the dipole moment $\vec{p}$: <br/><br/> $$\vec{p} = q \cdot \vec{d} = (0.01 \,\text{C})(0.4 \times 10^{-3} \,\text{m}) = 4 \times 10^{-6} \,\text{Cm}$$ <br/><br/> The dipole is placed in a uniform electric field $\vec{E}$ of magnitude $10 \,\text{dyne/C}$, which is equivalent to $10 \times 10^{-5} \,\text{N/C}$. <br/><br/> The angle between the dipole moment and the electric field is $30^{\circ}$. <br/><br/> The torque acting on the dipole can be calculated using the formula: <br/><br/> $\tau = pE \sin{\theta}$ <br/><br/> Substituting the given values: <br/><br/> $$\tau = (4 \times 10^{-6} \,\text{Cm})(10 \times 10^{-5} \,\text{N/C})\sin{30^{\circ}}$$ <br/><br/> $\tau = (4 \times 10^{-6} \,\text{Cm})(10^{-4} \,\text{N/C})(\frac{1}{2})$ <br/><br/> $\tau = 2 \times 10^{-10} \,\text{Nm}$ <br/><br/> The magnitude of the torque acting on the dipole is $2.0 \times 10^{-10} \,\text{Nm}$.