Physics 121: Electricity & Magnetism – Lecture 12

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

April 11, 2007 Center for Solar-Terrestrial Research

Gauss’ Law for Magnetic Fields

Gauss’ law

The simplest magnetic structure that can exist is a dipole. Magnetic mono-poles do not exist (as far as we know).

0B B dA

April 11, 2007 Center for Solar-Terrestrial Research

Magnetism and Electrons

Spin magnetic dipole moment

Bohr magneton

Orbital magnetic dipole moment

s

eS

m

249.27 10 J/T4B

eh

m

ext , exts s zU B B

orb orb2

eL

m

orb ext orb, extzU B B

April 11, 2007 Center for Solar-Terrestrial Research

Paramagnetism: A paramagnetic material placed in an external magnetic field develops a magnetic dipole moment in the direction of . If the field is non-uniform, the paramagnetic material is attracted toward a region of greater magnetic field from a region of lesser field.

Magnetic MaterialsDiamagnetism: A diamagnetic material placed in an external magnetic field develops a magnetic dipole moment directed opposite . If the field is non-uniform, the diamagnetic material is repelled from a region of greater magnetic field toward a region of lesser field.

extB

extB

extB

extB

April 11, 2007 Center for Solar-Terrestrial Research

Ferromagnetism

A ferromagnetic material placed in an external magnetic field develops a strong magnetic dipole moment in the direction of . If the field is non-uniform, the ferromagnetic material is attracted toward a region of greater magnetic field from a region of lesser field.

Magnetization curve and hysteresis loop

extB

extB

April 11, 2007 Center for Solar-Terrestrial Research

Induced Magnetic Fields

Maxwell’s law of induction

Ampere-Maxwell law

0 0Ed

B dsdt

0 0 0 encEd

B ds idt

April 11, 2007 Center for Solar-Terrestrial Research

Displacement Current

Displacement current

Ampere-Maxwell law

Inside a circular capacitor

Outside a circular capacitor

022diB rR

,enc 0E

d

di

dt

0 ,enc 0 encdB ds i i

0

2diBr