magnetism-and-matter Question 1
Question: Q. 1. A toroid of $n$ turns, mean radius $R$ and crosssectional 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.
[NCERT Exemplar]
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Solution:
Ans. Correct option : (c)
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 torol, the magnetic field $B$ is zero because the netseurrent 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.
