Explanation (Complete Step by Step Calculation)
Torque on a magnetic dipole placed in a uniform magnetic field is given by:
\[
\tau = m B \sin\theta
\]
Given torque:
\[
\tau = 0.016 \, \text{N·m}
\]
Magnetic field:
\[
B = 800 \, \text{Gauss} = 800 \times 10^{-4} = 0.08 \, \text{T}
\]
Angle:
\[
\theta = 30^\circ, \quad \sin 30^\circ = \frac{1}{2}
\]
Magnetic dipole moment:
\[
m = \frac{\tau}{B \sin\theta}
\]
\[
m = \frac{0.016}{0.08 \times 0.5}
\]
\[
m = \frac{0.016}{0.04} = 0.4 \, \text{A·m}^2
\]
Magnetic potential energy of a dipole in a magnetic field is:
\[
U = -mB\cos\theta
\]
At most stable position, \( \theta = 0^\circ \):
\[
U_{\text{min}} = -mB
\]
At most unstable position, \( \theta = 180^\circ \):
\[
U_{\text{max}} = +mB
\]
Work done in moving from stable to unstable position:
\[
W = U_{\text{max}} - U_{\text{min}} = 2mB
\]
\[
W = 2 \times 0.4 \times 0.08
\]
\[
W = 0.064 \, \text{J} = 64 \times 10^{-3} \, \text{J}
\]
Comparing with \( \alpha \times 10^{-3} \) J:
\[
\alpha = 64
\]
Hence, the value of \( \alpha \) is 64.