A flat circular coil of turns and radius carries a steady current

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

The Boundary-Value Problem, Ch The magnetic multipole expansion and the magnetic scalar potential

Problem

A flat circular coil of N=50N = 50 turns and radius r=0.020 mr = 0.020\,\mathrm{m} carries a steady current I=0.30 AI = 0.30\,\mathrm{A}. It sits in a uniform applied field B=0.40 TB = 0.40\,\mathrm{T}, current held fixed by an external source throughout. ((a)) Find the magnitude of the coil's magnetic moment. ((b)) The coil starts with its moment aligned with B\mathbf B (θ=0\theta = 0) and is turned to θ=90∘\theta = 90^\circ. Find the magnitude of the torque on the coil at θ=90∘\theta = 90^\circ. ((c)) Find the magnitude of the work an external agent must do (against the field) to turn the coil from θ=0\theta = 0 to θ=90∘\theta = 90^\circ, using U=−m⋅BU = -\mathbf m\cdot\mathbf B for the orientational energy.

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