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Introductory Physics Homework Help
Magnetic energy stored in a cylindrical conductor
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[QUOTE="Granger, post: 6016248, member: 574395"] [h2]Homework Statement [/h2] So I came across with following problem: > 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. [h2]Homework Equations[/h2] 3. The Attempt at a Solution [/B] So my question is more of a conceptual one. I proceeded to apply Ampere's law to calculate the B field which is \begin{cases} \frac{\mu_0Ir}{2\pi a^2} \,,\, r<a\\ \\ \\ \frac{\mu_0I}{2\pi r} \,,\, r>a\end{cases} I checked the resolution of the problem and they seem to only calculate the magnetic energy on the conductor. But according to $$\iiint_{all\,space} 0.5 B^2 \,dV$$ 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 $$\frac{\mu_0 I^2}{16 \pi}$$ I also have know idea on how to compute the integral outside the conductor. What limits of integration should I take? I'm really confused, can someone help me? [/QUOTE]
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Magnetic energy stored in a cylindrical conductor
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