Question

how might you measure the magnetic dipole moment of a compass needle??

Answer 1

here...as per ur question
If you can measure the magnetic field intensity and the torque it exerts on the needle then the equation
τ=mB
can be used . If you can't measure the torque directly you can always just measure the radius of the needle and the tangential acceleration and use the equation
If you can measure the magnetic field intensity and the torque it exerts on the needle then the equation
τ=(I/r)atangential
so here I is the moment of interia..