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AJKing
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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?