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,dltlt`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).

Options

A. `2 J T^(-1)`
B. `4 J T^(-1)`
C. `3 J T^(-1)`
D. `9 J T^(-1)`

Answer

A

Explanation

Magnetic moment of a current carrying loop, `vecmu = IvecS`
Area of the loop, `vecS = vec(AB) xx vec(BC)`
Here, `vec(AB) = -2d hati +2ahatj , vec(BC) = 2b hatk`
`therefore vecS=(-2d hati + 2a hatj) xx (2b hatk) = 4bd hati + 4ab hati`
`therefore |vecmu|= I|vecS|=4Ib sqrt(a^(2)+d^(2))`
`=4 xx 0.01 xx 10 xx sqrt(3^(2) + 4^(2)) = 0.4 xx 5 = 2J T^(-1)`