Question

A coil is composed of circular loops of radius \(r=5.13 \mathrm{~cm}\) and has \(N=47\) windings. A current, \(i=1.27 \mathrm{~A}\), flows through the coil, which is inside a homogeneous magnetic field of magnitude \(0.911 \mathrm{~T}\). What is the maximum torque on the coil due to the magnetic field? a) \(0.148 \mathrm{~N} \mathrm{~m}\) b) \(0.211 \mathrm{~N} \mathrm{~m}\) c) \(0.350 \mathrm{~N} \mathrm{~m}\) d) \(0.450 \mathrm{~N} \mathrm{~m}\) e) \(0.622 \mathrm{Nm}\)

Short answer

#form_short_answer# To find the magnetic moment of the coil, we first need to calculate the area of the circular loop, A = π * r². Then, we can use the formula μ = N * i * A to obtain the magnetic moment.

Step-by-step solution

Calculate the Magnetic Moment of the Coil

First, we need to find the magnetic moment of the coil. The magnetic moment (μ) of a loop can be calculated using the formula: μ = N * i * A where N is the number of windings, i is the current flowing through the coil, and A is the area of the loop. Since the loops are circular, the area can be calculated as: A = π * r² Let's plug in the given values and calculate the magnetic moment.