Q71 / 90 · JEE Main 2015 (04 Apr) · Physics

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) Figure (b) Figure

(c) Figure (d) 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?

  • A
    (b) and (c), respectively.
  • B
    (a) and (b), respectively.
  • C
    (a) and (c), respectively.
  • Correct answer
    D
    (b) and (d), respectively.

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→=-MBcosθ

When M→ is in the same direction as B→ then τ→=0 and U is minimum = -MB as θ=0o.⇒ Stable equilibrium is (b).

When M→ the opposite direction of B→, then τ→=0 and U is max = +MB
As, θ=180o ⇒Unstable equilibrium in (d)

Hence, the correct answer is option: 'D'.

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