Inductance in a straight wire

  • Thread starter AJKing
  • Start date
  • #1
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Homework Statement



A long wire carries a current i uniformly distributed over a cross section of the wire.

Show that the magnetic energy of a length l equals μ_0 i2 l / 16π. Describe why this doesn't depend on diameter.

Show that the inductance for a length of the wire l associated with the flux inside the wire is μ_0 l / 8π

Homework Equations



u_B = B2/2μ_0

U = L i2 /2

Biot-Savart law for Field in a long wire:

B = μ_0 i / 2 π r


The Attempt at a Solution



Solve for u_B as

u_B = B2/2μ_0

= (μ_0 i / 2 π r ) 2 / 2μ_0

Multiply by volume of wire to find U:

U = ( (μ_0 i / 2 π r ) 2 / 2μ_0 ) * π r^2 l

= μ_0 i2 l / 8π

I'm off by a factor 1/2. Any suggestions?
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
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You need to find B inside the wire.

If uB is not uniform inside, integration will be necessary to find the total energy.
 

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