Potential energy

Question

A magnetized sewing needle has a magnetic moment of 9.70x10−3Am2 . At its location, the Earth’s magnetic field is 55.0 T northward at 48.0o below the horizontal. Identify the orientations of the needle that represent (a) the minimum potential energy and (b) the maximum potential energy of the needle–field system. (c) How much work must be done on the system to move the needle from the minimum to the maximum potential energy orientation

Answer 1

πτ = mXB ... torque = magnetic moment cross magnetic field

m= 9.7E-3 A-m², also J/T, B= 55µT = 55E-6 T

a) Torque = 0 if needle is allowed to point down and North, then this is minimum energy.

b) for maximum energy the needle would be forced to point South (rotate π) and down at 48 degrees equal to

9.7E-3*55E-6=534E-9 Joules

c) Work required = 534E-9πJ