The given figure shows two magnetized needles and a magnet P with their magnetic moments, shown with the arrow sign. Which of the following statements are correct in respect of this configuration?

(A) $Q_1$ is in stable equilibrium
(B) $Q_2$ is in unstable equilibrium
(C) $Q_1$ is in unstable equilibrium
(D) $Q_2$ is in stable equilibrium

Choose the correct answer from the options given below:

(A) and (B) only

The correct answer is Option (1) → (A) and (B) only

Correct options: (A) and (B)

Magnetic potential energy: $U=-\vec{m}\cdot\vec{B}=-mB\cos\theta$. Minimum (stable) when $\theta=0$ (parallel), maximum (unstable) when $\theta=\pi$ (antiparallel).

At Q1 the needle's magnetic moment is parallel to the local field $\vec{B}$ → $\theta=0$ → stable.

At Q2 the needle's magnetic moment is antiparallel to the local field $\vec{B}$ → $\theta=\pi$ → unstable.