First part done in lecturers:

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• First part done in lecturers

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• The circular disk can be deduced from previous
  result
• Think of disk as being made up of a series of
  rings thickness dR

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m
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2
2
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Let qZe
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Look for a particular solution

• This particular solution will correspond to
• The displacement from equilibrium

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The Hall Effect
w
Consider a flat strip of material,
width,w Carrying a current I. By convention the
current flows from ve to ve. Suppose the
current is carried by carriers, charge,q.A
uniform magnetic field,B is established
perpendicular to the plane of the strip.
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The Hall Effect
w
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Magnetic Vector Potentials
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Question
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• Hence

of Poissons
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• We have shown that there exists a solution A s.t.

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In cartesian coordinates
3 sets of Poissons equations
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• We may assume J goes to zero at infinity
• Then we can solve

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Electric dipole
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Multipole expansion of the vector potential

• Idea we are looking for an approximate formula
  for a localized current distribution
• We will write the potential in powers of 1/r
• Keep the highest non vanishing contribution

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2
2
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quadrapole
monopole
dipole
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Vector Potential a large distance from a closed
current loop
Monopole dipole
quadrapole
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Force, Torque on current loop
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