question_answer

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

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

B) points along the axis of the toroid \[(m={{m}_{\phi }})\]

C) is zero, otherwise there would be a field falling as \[\frac{1}{{{r}^{3}}}\] at large distances outside the toroid.

D) is pointing radially outwards.

Correct Answer: C

Solution :

Option [c] is correct.

Explanation: As we know that a toroid can be considered as a ring shaped closed solenoid. So that it is like an endless cylindrical solenoid.

So, 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. So that, the magnetic moment of toroid is zero. In general, if we take r as a long distance outside the toroid, the \[m\propto \frac{1}{{{r}^{3}}}\] but this case is not possible here.