Ncert Exercises & Solutions

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 XY-plane. Its magnetic moment m:

1.	is non-zero and points in the z-direction by symmetry
2.	points along the axis of the toroid ( $m = m\vec{\phi}$ )
3.	is zero, otherwise, there would be a field falling as $\frac{1}{r^{3}}$ at Lange distances outside the toroid
4.	is pointing radially outwards

Step 1: In the case of the toroid, the magnetic field is only confined inside the body of the toroid in the form of concentric magnetic lines of force and there is no magnetic field outside the body of the toroid. This is because the loop encloses no current. Thus, the magnetic moment of the toroid is zero.

Step 2: In general, if we taker as a large distance outside the toroid, then m

$\propto \frac{1}{r^{3}}$ . But this case is not possible here.

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