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# F16 PH333 6.3.1-6.3.3

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## Richard Datwyler

on 28 November 2018

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#### Transcript of F16 PH333 6.3.1-6.3.3

The H Field

6.3.1 The H Field
6.3.2 Parallel
6.3.3 Boundary Conditions

Amperes Law in Magnetized Material
Now that we have the Bound Currents,
we can get the total currents as
These brings back what Ampere's Law need to be.
or for convenience define
rewriting Ampere's Law gives
These two equations then are the magnetostatics analogous terms to electrostatics electric displacement D and Gauss's law
The H field is from both the external field which come from currents we turn on directly, and those that are born from magnetizing the object inducing bound currents
This H field is what is most frequently referred to by experimentalists, because it is what is actually measured. The B field can be calculated from it, but you need to know the substance to subtract off the magnetization effects.
A long copper rod of radius R carries a uniformly distributed (free) current I, Find H inside and outside.
I
B
Copper is Diamagnetic so the bound current will make M go clockwise. But H and B will be counter Clockwise.
Make an Amperian loop both inside and outside.
K
J
b
b
gives
if desired B outside
Note
Unlike Gauss's law in determining the D and E
Ampere's law isn't enough. We need to know the divergence as well
from

In a bar magnet, with no free current, yet a permantent magnetization M, MIGHT make you think H=0 if so then inside. Then B=0 outside (not so).
Look for symmetry, if it exists (cylindrical, plane, solenoid, or toroid) then and H is made from free currents only.
Boundary conditions
Using both Amperian loops and Gaussian surfaces, through a boundary we get:
or looking at B by itself (theoretically easy, experimentally hard)
Now, practice some of this with the homework
1
8
12

H
M
"Could you please explain section 6.3.2?"
"So H is the magnetic field produced inside of a material?"
"The new nameless variable H remains mysterious too me "

"What is the physical representation of H and does it have a formal name?"
Full transcript