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F16 PH333 5.4.1-5.4.3

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Richard Datwyler

on 19 November 2018

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Transcript of F16 PH333 5.4.1-5.4.3

Magnetic Vector Potential
5.4.1 Vector Potential
5.4.2 Boundary Conditions
5.4.3 Multipole Expansion
Vector Potential
Just as with Electrostatics the curl of E opened up a scalar potential, in magnetostatics the diverges opens up a Vector potential
divergence gives 0
curl gives:
This is same format as Poisson's and thus yields A
A (a bit more)
Typically A will be the same direction as the current
This equation is really 3 equations
Summary and BC
(note, opposite of E)
Multipole Expansion
following the same expansion technique for electric dipoles we can find A being composed of monopole, dipole, quadrupole... terms
1 / script r is the generating function
this monopole term is always zero. comes from B being divergenceless. and second term is:
with
example of A # 23
example of m # 35
Once you find A then a good check is that is it divergenceless, and then to find B.
what current density would produce
use cylindrical coordinates.
compute this!
and
compute this!
note in same direction as A
find magnetic dipole moment of record radius R carrying uniform surface charge sigma and rotating at constant angular velocity
What is the dipole term for the vector potential?
What is the magnetic field approximately (long ways away)
"Can you please help me to visualize the parallel discontinuity across a boundary in electromagnetics?
"I'm having some trouble visualizing what A physically represents."
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