5.3 Divergence and Curl of B Ampere’s law differential form.

5.3 Divergence and Curl of B

0 B

Ampere’s lawdifferential form

JB o

Drawing magnetic field lines:

The lines are closed or go to infinity.

The lines encircle the current. I

The lines are perpendicular tothe current.

For current distributions, decompose into wires and use superposition.

Direction from the right-hand rule

enclo

loop

Id lB

Ampere’s lawintegral form

Simple solutions for:Infinite straight linesInfinite planesInfinite solenoidsToroids

Example 5.7 – Straight Wire

Field of a straightwire.

Example 5.8 – Uniform Surface Current

Example 5.9 –Long Solenoid

Example 5.8 –Toroidal Coil

Tokamak Nuclear Fusion Reactor

Maxwell’s equations for electro- and magnetostatics

)(

0

0

0

0

0

BvEF

B

E

JB

B

E

Eo

Q

Gauss’s law

Ampere’s law

Far from charges

Far from currents

Lorentz force