Antepolleo
Dec6-05, 09:23 PM
It's electromagnetics time again.
I'm horribly stuck on a homework problem. It has to do with mutual inductance, and I know how the problem works conceptually, but I'm having a difficult time with the mathematics. The problem:
A very long (read: infinite) wire is a distance d from the center of a conducting circular loop of radius b. Find the mutual inductance between them.
I know, by Ampere's law, the the magnetic flux density of the wire will be
\vec{B}=\frac{\mu_{0}I}{2 \pi r}\hat{a}_{\phi}
With r being the distance from the wire. I know this will cause a magnetic flux to pass through the surface enclosed by the circular loop, and it will not be uniform. I can't for the life of me figure out how to put this in mathematical terms. I'm pretty sure I need to use this:
\phi = \int_{S}\vec{B} \cdot d \vec{s}
But I'm not sure where to put the differential, or even which coordinate system to use.
I'm horribly stuck on a homework problem. It has to do with mutual inductance, and I know how the problem works conceptually, but I'm having a difficult time with the mathematics. The problem:
A very long (read: infinite) wire is a distance d from the center of a conducting circular loop of radius b. Find the mutual inductance between them.
I know, by Ampere's law, the the magnetic flux density of the wire will be
\vec{B}=\frac{\mu_{0}I}{2 \pi r}\hat{a}_{\phi}
With r being the distance from the wire. I know this will cause a magnetic flux to pass through the surface enclosed by the circular loop, and it will not be uniform. I can't for the life of me figure out how to put this in mathematical terms. I'm pretty sure I need to use this:
\phi = \int_{S}\vec{B} \cdot d \vec{s}
But I'm not sure where to put the differential, or even which coordinate system to use.