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 $\overline{M}$ is

• A. is non-zero and points in the z-direction by symmetry
• B. points along the axis of the toroid $(\overline{M}=M\hat{\varphi })$
• C. is zero, otherwise there would be field falling as $\frac{1}{r^3}$ at large distances outside the toroid
• D. is pointing radially outwards

Answer 1

Answer: (C)

is zero, otherwise there would be field falling as $\frac{1}{r^3}$ at large distances outside the toroid

Key concept:- Toroid'. A toroid can be considered as a ring-shaped closed solenoid. Hence it is like an endless cylindrical solenoid.

REF. IMAGE

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.

In general, if we take r as a large distance outside the toroid, then $m\propto \frac{1}{r^3}$. But this case is not possible here.