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Part of JMAG-01 — Magnetic Effects: Biot-Savart & Ampere's Law

Magnetic Moment and Torque on a Loop

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Magnetic moment of a current loop: m⃗=NIA⃗\vec{m} = NI\vec{A} (direction: right-hand rule with current). Torque in uniform field: τ⃗=m⃗×B⃗\vec{\tau} = \vec{m} \times \vec{B}, magnitude τ=mBsin⁡θ\tau = mB\sin\theta. Potential energy: U=−m⃗⋅B⃗=−mBcos⁡θU = -\vec{m} \cdot \vec{B} = -mB\cos\theta. Stable equilibrium: θ=0\theta = 0 (m⃗∥B⃗\vec{m} \parallel \vec{B}). Unstable: θ=π\theta = \pi. Work done to rotate from θ1\theta_1 to θ2\theta_2: W=mB(cos⁡θ1−cos⁡θ2)W = mB(\cos\theta_1 - \cos\theta_2).

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