A circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is

Step-by-step solution

Let l bet he length of metal wire. When wire is bent into a circular coil of radius r, then r = l 2 π ∴ A r e a , A = π l 2 π 2 = π l 2 4 π 2 ∴ Magnetic dipole moment associated with circular coil, μ c = i A = i π l 2 4 π 2 μ c = i l 2 4 π … (i) When metal wire is bent into a square coil then side of square a = l 4 ∴ A r e a , A = a 2 = l 2 16 ∴ Magnetic dipole moment associated with square coil, μ s = i A = i l 2 16 ∴ μ c μ s = i l 2 4 π i l 2 16 = 16 4 π = 4 π Hence, the ratio of magnetic dipole moment of circula