Two circular concentric loops of radii `r_(1)=20cm, r_(2)=30 cm` are placed in the `X-Y` plane as shown in the figure. A current I= 7 A is flowing through them. The magnetic moment of this loop system is

Options

A. `+4.0 hatk (Am^(2))`
B. `-1.5 hatk (Am^(2))`
C. `+1.1 hatk (Am^(2))`
D. `+1.3 hatj (Am^(2))`

Answer

C

Explanation

`vecm = I vecA`
`vecm_(1) = I pi r_(1)^(2) (-hatk) = -7 xx pi xx (0.2)^(2) (hatk)`
`vecm_(2) = I pi r_(2)^(2) (hatk) = +7 xx pi xx (0.3)^(2) (hatk)`
`vecm_("net") = vecm_(2) + vecm_(1) = 7 xx (22)/(7) [ (0.3)^(2) - (0.2)^(2)] hatk`
`1.1 hatk (Am^2)`