A toroid of \( n \) turns, mean radius \( R \) and cross-sectional ...

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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
\( \mathrm{P} \) \( x \) - \( y \) plane. Its magnetic moment \( \mathbf{m} \)

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(a) is non-zero and points in the \( z \)-direction by symmetry.
(b) points along the axis of the tortoid \( (\mathbf{m}=m \hat{\phi}) \).
(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.
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