Ampere’s Law

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Amperes Law

• Alan Murray

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Try this
Create a contour for integration (a circle seems
to make sense here!)
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òH.dl Current Ienclosed

• This is, as it turns out, Amperes Law and is the
  magnetic-field equivalent of Gausss law
• If we define HBµ, BµH, thenòH.dl Current
  enclosed òòòJ.ds

I4
I5
I1
I3
I2
I6
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òH.dl Current Ienclosed
I4
I1
I3
I2
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Amperes Law Worked Example

• Calculate the magnetic field H both
• Outside (rgtR)
• and
• Inside (rltR)
• A wire with uniformly-distributed current
  I,current density

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Outside rgtR, òH.dl Ienclosed
B
r
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Inside rltR, òH.dl Ienclosed
B?
R
r
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Inside rltR, òH.dl Ienclosed
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Ampere Worked example
i.e. what is the magnetic fieldabove and close
to a metal trackon a printed circuit board or
chip?
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What does the B-field look like?
B-field lines
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òH.dl Ienclosed?
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òH.dl Ienclosed?
H
a
b
b
a
Current enclosed aI/L òH.dl aH aH
2aH òH.dl Ienclosed 2aH aI/L H _I_
2L
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òH.dl Ienclosed?
H -I_ 2L
H I_ 2L