A conductor carries a constant current I along the closed path abcdefgha involving 8 of the 12 edges of length `l`. Find the magnetic dipole moment of the closed path.

Options

A. `l^(2)Ihat(j)`
B. `l^(3)Ihat(j)`
C. `l^(4)Ihat(j)`
D. `l^(5)Ihat(j)`

Answer

A

Explanation

The closed path is a super positiion of three loops`: ` bcfgb, abgha and cdefc.

The magnetic moment of the each loops are `:`
Loop `" "1bcfgb" "vec(mu_(1))=l^(2)Ihat(j)`
`2abgha " "vec(mu_(2))=-l^(2)Ihat(i)`
`3 cdefc" "vec(mu_(3))=l^(2)Ihat(i)`
The total magnetic moment is
`vec(mu)=vec(mu_(1))+vec(mu_(2))+vec(mu_(3))" or "vec(mu)=l^(2)Ihat(j)` .