The Maxwell�’s Equations

in cgs units

original Maxwell�’s equations

magnetic monopoles

magnetic vector potential

magnetic field momentum

Magnetic moment

Magnetic moment of a closed loop carrying current I:2i

C

I d ISc

M r l nC

Magnetic field on the axis of a loop of radius R at a distance z is: 3/ 22 2

2 iz

MHR z

Total magnetic moment: iM M (superposition principle)

origin of magnetism (except for currents�…)

ion BgM J J gyromagnetic ratiog �– Landé factor

J L S

spin

g219.27410 10

2Be ergmc G

Bohrmagneton

total angular momentumorbital

spin1 1 1

12 1

J J S S L Lg

J J

free electron:

2.0023 2.00g

Magnetic moment:g

e BM

(J=S=1/2)(J=S=1/2)

magnetic moment in a magnetic field

torque: cosW BBEnergy:

B

BF grad W grad BForce:

B for example, for ,0,0 , , ,0x x yB xB

BB xxdBFand

in inhomogeneous magnetic field

x xBB x dx

0x 0x

F F h i

B B

F changes signhowever torque aligns along the field