A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is:

<p>Given:</p> <p><p>Potential difference $ V = 5 \, \text{V} $</p></p> <p><p>Separation between the plates $ d = 0.5 \, \text{mm} = 0.5 \times 10^{-3} \, \text{m} $</p></p> <p>The electric field $ E $ is calculated as:</p> <p>$ E = \frac{V}{d} = \frac{5}{0.5 \times 10^{-3}} = 10^4 \, \text{V/m} $</p> <p>The torque $ \tau $ experienced by the dipole in the electric field is given by:</p> <p>$ \tau = PE \sin \theta $</p> <p>Where:</p> <p><p>$ P $ is the dipole moment,</p></p> <p><p>$ E $ is the electric field,</p></p> <p><p>$ \theta = 30^\circ $ is the angle of rotation.</p></p> <p>The dipole moment $ P $ is calculated by:</p> <p>$ P = q \times a = (2 \times 10^{-6} \, \text{C}) \times (0.5 \times 10^{-6} \, \text{m}) = 1 \times 10^{-12} \, \text{C} \cdot \text{m} $</p> <p>Substituting the values into the torque equation:</p> <p>$ \tau = (1 \times 10^{-12} \, \text{C} \cdot \text{m}) \times 10^4 \, \text{V/m} \times \sin 30^\circ $</p> <p>Since $\sin 30^\circ = 0.5$, the torque simplifies to:</p> <p>$ \tau = 1 \times 10^{-12} \times 10^4 \times 0.5 = 5 \times 10^{-9} \, \text{N} \cdot \text{m} $</p> <p>Thus, the torque is $ 5 \times 10^{-9} \, \text{N} \cdot \text{m} $.</p>