Question

A toroid of n turns, mean radius R and cross-sectional radius a carries current I. It is placed on a horizontal table taken as x-y plane. Its magnetic moment m ______.

Options

• is non-zero and points in the z-direction by symmetry.

• points along the axis of the tortoid (m = m `hatφ`).

• is zero, otherwise there would be a field falling as `1/r^3` at large distances outside the toroid.

• is pointing radially outwards.

Answer 1

A toroid of n turns, mean radius R and cross-sectional radius a carries current I. It is placed on a horizontal table taken as x-y plane. Its magnetic moment m is zero, otherwise there would be a field falling as `1/r^3` at large distances outside the toroid.

Explanation:

A toroid can be considered a ring-shaped closed solenoid. Hence it is like an endless cylindrical solenoid.

The magnetic field is only confined inside the body of a toroid in the form of concentric magnetic lines of force. For any point inside the empty space surrounded by toroid and outside the toroid, the magnetic field B is zero because the net current enclosed in these spaces is zero. Thus, the magnetic moment of toroid is zero.