Question

A circular coil of 195 turns has a radius of 2.73 cm. (a) Calculate the current that results in a magnetic dipole moment of magnitude 2.23 A⋅m². (b) Find the maximum magnitude of the torque that the coil, carrying this current, can experience in a uniform 37.4mT magnetic field.

Answer 1

To calculate the required current for a specific magnetic dipole moment, the formula m = NIA is used, with m as the moment, N the number of turns, I the current, and A the area. For torque, the formula τ = mB applies, with τ the torque, m the dipole moment, and B the magnetic field strength.

Step-by-step explanation:

A student has inquired about the calculation of current resulting in a specific magnetic dipole moment for a circular coil, and the maximum torque that the coil can experience in a uniform magnetic field. To address part (a) of the question, the formula for the magnetic dipole moment (m) of a circular coil is given by m = NIA, where N is the number of turns, I is the current, and A is the area of the coil. The area A of the coil with radius r is calculated as A = πr^2. Setting the dipole moment to the value given (2.23 A·m²), we can solve for the current I.

For part (b), the maximum torque (τ) that a coil can experience is given by τ = mB, where m is the magnetic dipole moment of the coil and B is the strength of the external magnetic field. Here, m is the dipole moment calculated previously, and B is given as 37.4 mT.