Answer
See answers.
Work Step by Step
a. An individual loop of wire creates a magnetic field along its axis. Consider path 1. We see that symmetry demands a magnetic field that has the same strength anywhere along the path, and which is parallel (tangent) to the circular path.
The net current through the area enclosed by path 1 is NI, because every wire penetrates the area once. Use equation 20–9.
$$B(2\pi R)=\mu_o NI$$
$$B=\frac{\mu_o NI }{2\pi R }$$
b. The net current through the area enclosed by path 2 is 0, because every wire penetrates the area twice: once going out of the page, and once going into the page. Use equation 20–9.
$$B(2\pi R)=\mu_o (0)$$
$$B=0$$
c. We see from part A that the field inside a toroid is not uniform. The field strength varies inversely with the distance from the center. The B field is strongest near the toroid's inside wall, and is weakest near the toroid’s outside wall.
