A circular coil with 50 turns and a radius of 2.0 cm carries a 5.0 A current while rotating in a magnetic field of strength 0.20 T . Determine the maximum torque exerted on the coil.

Step-by-step solution

The maximum torque on a current-carrying coil in a magnetic field is given by the formula: _ max = NIAB where: N is the number of turns = 50 I is the current = 5.0 A A is the area of the coil = r^2 = (2.0 10⁻² m )^2 = 4 10⁻⁴ m ^2 B is the magnetic field = 0.20 T Substituting the given values: _ max = 50 5.0 (4 10⁻⁴) 0.20 _ max = 250 0.20 4 10⁻⁴ _ max = 50 4 10⁻⁴ _ max = 200 10⁻⁴ _ max = 2 10⁻² 2 3.14 10⁻² = 6.28 10⁻² N m Rounding to two significant figures, we get 6.3 10⁻² N m .