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

(a) Given, 
Magnetic field along the positive z-direction = 3000 G = 3000 x 10^–4 T = 0.3 T
Current carried by the loop, I = 12 A
Area of rectangular loop, A = 10 x 5 cm² 
                                      = 50 x 10^–4 m²

Torque on the loop is given by,
                  $\boxed{\mathrm{\tau } = \mathrm{BIA} \cos \mathrm{\theta }}$ 

where, θ is the angle between the plane of loop and direction of magnetic field.
Here, θ = 0° . 

Therefore, torque is, τ = 0.3 x 12 x 50 x 10^–4 
                                = 1.8 x 10^–2 Nm. 

Using Fleming's left hand rule we can say that the direction of torque is along negative y direction. 

(b) The torque acting is the same as in case (a) but, the direction of torque is along side 10 cm. 

(c) The magnitude of torque is equal to 1.8 x 10^–2 Nm along - x direction of torque on lower arm of 5 cm towards – y axis.
(d)    This case is similar to (c). Direction of torque is 60°.
(e)    zero. (∵ angle between plane of loop and direction of magnetic field is 90°)
(f)    zero. 

Force is zero in each case. Stable equilibrium is corresponded by case (e).