A rectangular loop of sides 10 cm and 5 cm , carrying a current I of 12 A , is placed in different orientations as shown in the figure below. (a) (b) (c) (d) 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?

Step-by-step solution

For a magnetic dipole placed in a uniform magnetic field, the torque is given by τ → = M → × B → , and potential energy U is given as, U = - M → · B → = - M B cos θ When M → is in the same direction as B → then τ → = 0 and U is minimum = - M B as θ = 0 o . ⇒ Stable equilibrium is (b). When M → the opposite direction of B → , then τ → = 0 and U is max = + M B As, θ = 180 o ⇒ Unstable equilibrium in (