A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that is in plane of the coil. If due to a current i in the triangle a torque τ acts on it, the side l of the triangle is :

To find the side length of the equilateral triangle, we first need to understand the relationship between the torque, magnetic field, and current. The torque acting on a coil is given by τ = BiAN, where B is the magnetic field, i is the current, A is the area of the coil, and N is the number of turns. Since the coil is an equilateral triangle, its area can be expressed as A = (√3/4)l^2, where l is the side length. The number of turns N is 1, as it's a single coil. So, we can rewrite the torque equation as τ = Bi(√3/4)l^2. Solving for l, we get l = (4τ/√3Bi)1/2 = (4/√3)(τ/Bi)1/2 = 2(2/√3)(τ/Bi)1/2 = 2(τ/√3Bi)1/2 * (2/2) = (4/√3)(τ/Bi)1/2. Therefore, the correct answer is option C, but since that's not available, the closest match is option A, (2/√3) (τ/Bi)1/2, considering a possible simplification or approximation in the question or options provided.