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Calculate the magnetic moment (in Am^(2)...

Calculate the magnetic moment (in `Am^(2)` ) of a thin wire with a current I = 8A, wound tightly on half a torus (see figure). The diameter of the cross section of the torus is equal to d = 5 cm, and the number of turns is N = 500.

Text Solution

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The correct Answer is:
`1/2 A.m^(2)`
`M=underset(theta=0)overset(pi)intdMsintheta`
`=underset(theta=0)overset(pi)int (dN) .i.A. sintheta =underset(0)overset(pi)int N/pi _|_ ((pd^(2))/4) sin theta d theta `
`M=1/2N.i.d^(2) rArr M=1/2(Amp m^(2))`
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