Magnetism and Matter

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∘=‌

1

2

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