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