Verified Solution • 2025–26 Session moderate

QPages 228-229: Q9: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 228-229: Q9 Solution: The torque on a current loop is zero if the angle between the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that any orientation where the torque vanishes (θ=0 or 180°) is automatically a stable equilibrium; they must instead examine the magnetic dipole’s potential energy $U=-\vec m\cdot\vec B=-mB\cos\theta$ and verify that $\theta=0$ gives a minimum (stable) while $\theta=\pi$ gives a maximum (unstable).

The torque on a current loop is zero if the angle between the positive normal and the magnetic field is either θ=0\theta = 0 or θ=180∘\theta = 180^\circ. In which of the two orientations, the equilibrium is stable?

Step-by-Step Verified Solution

**Answer:** The equilibrium at θ=0\theta = 0 is stable. **Step-by-Step Explanation:** The potential energy of a magnetic dipole in a magnetic field is U=−m⃗⋅B⃗=−mBcos⁡θU = -\vec{m} \cdot \vec{B} = -mB\cos\theta. At θ=0\theta = 0, U=−mBU = -mB (minimum energy), so this is the stable equilibrium. At θ=180∘\theta = 180^\circ, U=+mBU = +mB (maximum energy), so this is unstable.

All Questions in this Chapter

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