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 figures below:
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?abcd
(A)(a) and (c), respectively
(B)(b) and (d), respectively✓ Correct
(C)(b) and (c), respectively
(D)(a) and (b), respectively
Answer: (B)
Solution
A current loop feels a torque τ=IA×B and stores energy U=−IA⋅B, so it rests in equilibrium only when its area vector lines up with the field, parallel or antiparallel. Among the orientations drawn, those are the two whose normal points along the z-axis. With the area vector along +z^, parallel to the field, the energy is least, so orientation (b) is the stable one; with it along −z^, antiparallel, the energy is greatest, so orientation (d) is in unstable equilibrium.
JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option