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A current I flows in a rectangularly sha...

A current I flows in a rectangularly shaped wire whose centre lies at `(x_0,0,0)` and whose vertices are located at the points A `(x_0+d,-a,-b),B(x_0-d,a,-b),C(x_0-d,a,+b) and D(x_0+d,-a,b)` respectively. Assume that a,b,d << `x_0`. Find the magnitude of magnetic dipole moment vector of the rectangular wire frame in `J//T`. (Given, b=10 m,I=0.01A, d=4m,a=3m).

Text Solution

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The correct Answer is:
2
`vecm=I_2vecS`

`vecS=vec(BA)xxvec(AD), vec(BA)=2dhati-2ahatj, vec(AD)=2bhatk`
`vecS=2(dhati-ahatj)xx2bhatk`
`vecM=-4bI(dhatj+ahati) implies |vecM|=4bIsqrt(d^2+a^2)=2J//T`
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