A rectangular loop of sides 10cm and 5cm carrying a current I of 12A is placed in different orienctations as shown in the figure

If there is a uniform magnetic field of 0.3 T in the positive z-direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium .

Options

A. (2)and(4), respectively
B. (2)and(3), respectively
C. (1)and(2), respectively
D. (1)and(3), respectively

Answer

A

Explanation

`I=12A, vec(B)=0.3hatk T`,
`A=10xx5cm^(2)=50xx10^(-4)m^(2)`
`vec(M)=I Ahat(n)=12xx50xx10^(-4)hatn Am^(2)`
`6xx10^(-2)hat(n)Am^(2)`
`"Here", vec(M)_(1)=6xx10^(-2)hati Am^(2), vec(M_(2))=6xx10^(-2)Am^(2)`
`vec(M_(3))=-6xx10^(-2)hatj Am^(2), vec( M_(4))=-6xx10^(-2)hatk Am^(2)`
`vec(M_(2))` is parallel to `vec(B)`, it means potential energy is minimum, therefore in orientiation (2) the loop is in stbale equilibrium.
`vec(M _(4))` is antiparallel to `vec(B_(4))`, it means potential energy is maximum therefore in oriention (4) the loop is in unstbale equilibirum.