Question

A coil in the shape of an equilateral triangle of side \( l \) is suspended between two pole pieces of a permanent magnet, such that the magnetic field, \( B \), is in the 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

• A. \( 2 \left( \frac{t}{\sqrt{3} B I} \right)^{1/2} \)
• B. \( \frac{2}{\sqrt{3}} \left( \frac{I}{B l} \right) \)
• C. \( 2 \left( \frac{I}{B l} \right)^{1/2} \)
• D. \( \frac{1}{\sqrt{3}} \left( \frac{I}{B l} \right) \)

Hint:

The torque on a current-carrying coil in a magnetic field depends on the area of the coil, the current, and the angle between the coil's normal and the magnetic field.

Answer 1

The Correct Option is A

For a coil in the shape of an equilateral triangle, the torque \( \tau \) on the coil due to the magnetic field \( B \) is given by: \[ \tau = n B A I \sin(\theta) \] where \( n \) is the number of turns (in this case, \( n = 1 \) for a single turn), \( A \) is the area of the coil, \( I \) is the current, and \( \theta \) is the angle between the magnetic field and the normal to the coil’s plane. For an equilateral triangle, the area \( A \) is: \[ A = \frac{\sqrt{3}}{4} l^2 \] Substituting the known values and solving for the side length \( l \), we get the answer \( 2 \left( \frac{t}{\sqrt{3} B I} \right)^{1/2} \). 
Hence, the correct answer is (a).