Given:

Potential difference $ V = 5 \, \text{V} $

Separation between the plates $ d = 0.5 \, \text{mm} = 0.5 \times 10^{-3} \, \text{m} $

The electric field $ E $ is calculated as:

$ E = \frac{V}{d} = \frac{5}{0.5 \times 10^{-3}} = 10^4 \, \text{V/m} $

The torque $ \tau $ experienced by the dipole in the electric field is given by:

$ \tau = PE \sin \theta $

Where:

$ P $ is the dipole moment,

$ E $ is the electric field,

$ \theta = 30^\circ $ is the angle of rotation.

The dipole moment $ P $ is calculated by:

$ 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} $

Substituting the values into the torque equation:

$ \tau = (1 \times 10^{-12} \, \text{C} \cdot \text{m}) \times 10^4 \, \text{V/m} \times \sin 30^\circ $

Since $\sin 30^\circ = 0.5$, the torque simplifies to:

$ \tau = 1 \times 10^{-12} \times 10^4 \times 0.5 = 5 \times 10^{-9} \, \text{N} \cdot \text{m} $

Thus, the torque is $ 5 \times 10^{-9} \, \text{N} \cdot \text{m} $.