Magnetic Properties of Matter: Practice Problem & Solution
A coil in the shape of an equilateral triangle of side $L$ is suspended between the pole pieces of a permanent magnet such that $B$ is in plane of the coil. If due to a current $i$ in the triangle a torque $tau$ acts on it, the side $L$ of the triangle is : (2005)
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:
The magnetic moment is $M = i A = i \left( \frac{\sqrt{3}}{4} L^2 \right)$. The torque is $\tau = M B = i \frac{sqrt{3}}{4} L^2 B$. Solving for $L$ yields $2 \left[ \frac{\tau}{\sqrt{3}Bi} \right]^{1/2}$.
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