Magnetic moment of the bar magnet: M=104JT−1 Magnetic field: B=4×10−5T Initial orientation: θ1=0∘ (parallel to B ) Final orientation: θ2=60∘ Relevant concept The potential energy of a magnetic dipole in a magnetic field is U=−MB‌cos‌θ When the magnet is rotated slowly (quasi-statically), the work done by an external agent equals the change in potential energy of the system: ‌W=U2−U1=[−MB‌cos‌θ2]−[−MB‌cos‌θ1] ‌⇒W=MB(cos‌θ1−cos‌θ2) Substitute the values W=(104)(4×10−5)(cos‌0∘−cos‌60∘) Compute step by step: cos‌0∘=1,‌‌cos‌60∘=‌
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So, ‌W=(104)(4×10−5)(1−0.5) ‌W=(104)(4×10−5)(0.5) ‌W=(104×4×10−5×0.5) ‌W=(4×10−1×0.5)=0.2J