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# F16 PH 333 6.2.1-6.2.3

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## Richard Datwyler

on 27 November 2018

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#### Transcript of F16 PH 333 6.2.1-6.2.3

Field from a Magnetized object
6.2.1 Bound Currents
6.2.2 Physical meaning of Bound currents
6.2.3 B field inside matter
Bound currents
Now we will study the vector potential and define bound currents
Just as with electrostatics, finding the E field from a polarized object, we studied the potential and defined bound charge distributions.
using
with
So, what is this bound current
Just like lining dipoles top to bottom and having them cancel out, this only left the bits on the edges.
Same is true in magnetization, each little dipole near its neighbor will cancel out their internal contributions if the magnetization is uniform.
Conceptually, a single atom will have a current, but it is bound to the atom, but when placed next to similar currents, inside the object, the individual currents cancel, except for atoms at the very edge.
Bound currents
Conceptually I think we are about there.
This bound current is the addition of all the little currents in the atom being used together to make a surface current density on the outside
If the internal magnetization is not constant, then there will be a volume current density. Conservation of current ensure that the gradient of current density is zero.
Magnetic Field inside matter
Yet it can be shown that they indeed do, and the nature of the magnetic field outside and inside will be summed, and can be found using the two current distributions.
Inside, really close, things appear to be a problem. There are lots of different dipole moments that don't add up nicely.
An infinitely long circular cylinder carries a uniform magnetization M parallel to the axis. Find the Magnetic filed (due to M) inside and outside the cylinder.
this is just like a solenoid
So this results in
inside
outside B = 0
inside the cylinder constant value in z direction,
and zero outside.
M
"I am still not understanding the role the "A" plays. can we review this again?"
"Could you explain figure 6.18 please? I am not sure I understood their explanation in regards to it."
"how do the magnetic dipoles create the bound current? "
Looking at figure 6.15 with a slab of thickness t and constant M
I
M
t
a
K
but
thus
and to get the direction right
y
z
dz
M
M
z
z
M
y
M
y
'When we do the vector potential do we have to deal with higher terms like quadropole?'
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