Physics - Magnetic Dipoles etc.

Magnetic moment for a bar magnet

\overrightarrow{M}=m\overrightarrow{l}

m = magnetic pole strength

Magnetic moment for a current carrying loop

\overrightarrow{M}=NI\overrightarrow{A}

Torque experienced by a magnetic dipole

\overrightarrow{\tau}=\overrightarrow{M}✕\overrightarrow{B}=MB\sin\theta

M = magnetic moment

Torque experienced by a current carrying loop in a magnetic field

\overrightarrow{\tau}=NI\left(\overrightarrow{A}✕\overrightarrow{B}\right)=NIAB\sin\theta

“Torque is NIAB”

Energy stored in a dipole

U=-\overrightarrow{M}\cdot\overrightarrow{B}=MB\cos\theta

U=\Delta W

‘change in work done’

If area is halved, how does the pole strength of the dipole change

halved