Q. 1

# 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 .

C. is zero, otherwise there would be a field falling as at large distances outside the toroid.

D. is pointing radially outwards.

Answer :

A toroid is a donut shaped coil made up of insulated or wounded wire on its surface, the material of a toroid is usually powdered iron. A toroid acts as an inductor in electronic circuits, designated to places where large inductance is required mainly in low frequencies area.

Now here in the question it is asked if a toroid is kept on a horizontal table of radius R and it carries current I. In such a case the magnetic moment is:

Magnetic moments formed when charge flows in a circular path. Now the current flowing in cross sectional area, as area is a vector quantity and toroid is an object that can be said, is made up of multiple closed loops and each loop cancel the area vector of the another therefore, practically making the equivalent area vector zero. The formula for the magnetic moment is

where

is the current flowing, is the area of the object through which current is flowing.

Therefore, resulting in magnetic moment zero and a toroid has no definitive pole due to non-existence of outside magnetic field, making it zero again.

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