Rankers Physics

Magnetic Properties of Matter: Practice Problem & Solution

8. A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3}$ J of work to turn it through $60^{\circ}$. The torque needed to maintain the needle in this position will be: (2012 Mains)
$2\sqrt{3}$ J
$\sqrt{3}$ J
$3$ J
$\sqrt{3}/2$ J

Solution Explained:

To solve this problem, we apply the core principles of Magnetic Properties of Matter. Understanding the underlying formula is key to arriving at the correct answer below:

$W = MB(1 - \cos 60^{\circ}) = \frac{MB}{2} = \sqrt{3} \Rightarrow MB = 2\sqrt{3}$ J.
Torque, $\tau = MB \sin 60^{\circ} = 2\sqrt{3} \times \frac{\sqrt{3}}{2} = 3$ J.

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