A uniform magnetic field of `3000G` is established along the positive z-direction. A rectangular loop of sides `10cm` and `5cm` carries a current `12A`. What is the torque on the loop in the different cases shown in the figure. What is the force on each case? Which case corresponds to stable equilibrium?

Answer

(a) `1*8xx10^-2Nm` (b) Angle between area vector `vecA` and `vecB` is `0^@` or `180^@` (c) Loop will be in stable equilibrium if area vector `vecA` is parallel to magnetic field `vecB` and in unstable equilibrium when `vecA` is antiparallel to `vecB`

Explanation

Here, `B=3000G=0*3T`, `I=12A`
`A=10xx5=50cm^2=50xx10^-4m^2`.
(a) `tau_(max.)=IAB sin 90^@=12xx(50xx10^-4)xx0*3`
`=1*8xx10^-2Nm`
(b) Torque is zero when `sin theta=0` i.e. `theta=0^@` or `180^@`
(c) Loop will be in stable equilibrium if `vecA` is parallel to `vecB` and in unstable equilibrium if `vecA` is antiparallel to `vecB`.