Question

Expression for energy stored in current carrying conductor

Answer 1

Consider a cylindrical conductor of infinite length and circular section of radius a and that is traversed by a stationary current I. What is the magnetic energy stored in the conductor.

So my question is more of a conceptual one. I proceeded to apply Ampere's law to calculate the B field which is

⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪μ0Ir2πa2,r<aμ0I2πr,r>a

I checked the resolution of the problem and they seem to only calculate the magnetic energy on the conductor. But according to

∭allspace0.5B2dV

Shouldn't we take it all space? Because B isn't zero outside of the conductor. I'm so confused on why they just considered the conductor, am i misunderstanding something.

Also let me add that the integral in the cylinder gave us

μ0I216π

I also have know idea on how to compute the integral outside the conductor.

Answer 2

Answer:

Consider a cylindrical conductor of infinite length and circular section of radius a and that is traversed ...