A rectangular current loop (sides 10 cm and 5 cm, current I = 12 text A ) is placed in a uniform magnetic field B = 0.3 text T along +z. In which orientations is the loop in (i) stable equilibrium and (ii) unstable equilibrium?

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EEJ MAIN Physics QUESTION #7007

Question 1

A rectangular current loop (sides 10 cm and 5 cm, current $I = 12\ \text{A}$) is placed in a uniform magnetic field $B = 0.3\ \text{T}$ along $+z$. In which orientations is the loop in (i) stable equilibrium and (ii) unstable equilibrium?

(a) and (b) respectively
(a) and (c) respectively
(b) and (d) respectively✔️
(b) and (c) respectively

Correct Answer Explanation

Stable equilibrium: magnetic moment $\vec{m}$ is parallel to $\vec{B}$ (minimum energy, $U = -mB$).

Unstable equilibrium: $\vec{m}$ is antiparallel to $\vec{B}$ (maximum energy, $U = +mB$).

From the figures: In orientation (b), $\vec{m}$ is along $+z$ (parallel to $\vec{B}$) $\Rightarrow$ stable. In orientation (d), $\vec{m}$ is along $-z$ (antiparallel to $\vec{B}$) $\Rightarrow$ unstable. Answer: (b) and (d).

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