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,vecB=0.3hatKT`,
`A=10xx5cm^(2)=50xx10^(-4)m^(2)`
`vecM=Iahatn=-12xx50xx10^(-4)hatnAm^(2)=6xx10^(-2)Am^(2)hatn`
Here `vecM_(1)=6xx10^(-2)hatiAm^(2), vecM_(2)=6xx10^(-2)hatkAm^(2)`
`vecM_(3)=-6xx10^(-2)hatjAm^(2), vecM_(4)=-6xx10^(-2)hatkAm^(2)`
`vecM_(2)` is parallel to `vecB`, it means potential energy is minimum, therefore in orientation (2) the loop is in stable equilibrium. `vecM_(4)` is antiparallel to `vecB` it means potential energy is maximum, therefore in orientation (4) the loop is in unstable equilibrium.