Question

A toroid with a square cross section carries current i. The magnetic field has its largest

magnitude:
A. at the center of the hole
B. just inside the toroid at its inner surface
C. just inside the toroid at its outer surface
D. at any point inside (the field is uniform)
E. none of the above

Answer 1

The magnetic field inside a toroid has its largest magnitude just inside the toroid at its inner surface, due to the greater number of turns per unit length at a smaller circumference.

Step-by-step explanation:

The question pertains to the magnetic field inside a current-carrying toroid which is known to vary inversely with the distance from the axis. However, when the central radius is much larger compared to the cross-sectional diameter, the variation is minimal. For a toroid with a square cross-section, the magnetic field is not perfectly uniform but it can be approximated as such when certain conditions are met. The correct answer to where the magnetic field has its largest magnitude is B. just inside the toroid at its inner surface, since the magnetic field in a toroid is directly proportional to the number of turns per unit length, which is greater at the inner radius due to the smaller circumference.