A magnetic needle is in the most stable equilibrium state in a uniform magnetic field requires "W" units of work to turn through 60°. The work done to turn the magnetic needle from the position of most stable equilibrium to the most unstable equilibrium position is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4W
The potential energy of a magnetic dipole in a uniform field is \( U = -mB\cos\theta \). The work needed to turn it from angle \( \theta_1 \) to \( \theta_2 \) is the change in potential energy, and the stable equilibrium is at \( \theta = 0^\circ \).
\( W = U(60^\circ)-U(0^\circ) = mB(1-\cos60^\circ) = \frac{mB}{2} \Rightarrow mB = 2W \)
The most unstable equilibrium is at \( \theta = 180^\circ \).
\( W' = U(180^\circ)-U(0^\circ) = mB(1-\cos180^\circ) = 2mB = 2\times2W = 4W \)