- #1
KleZMeR
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Homework Statement
Infinite wire on Z axis
Loop radius a lies in x,z plane, centered on positive x axis, with center a distance b away from origin.
Find flux through loop.
Homework Equations
B field => from the infinite wire, dependent on 1/rho, in the (phi) direction, = (UoI/2pi)*(1/rho)
flux = (B dot dA), where dA is normal to plane, so in the (Y) direction
The Attempt at a Solution
If am attaching my attempt. What I have done so far, is figured out my B (dot) dA, by taking (phi) from B field and changing it to cartesian, and dotting it with differential area of my loop, which is in (Y) direction, so my (X) component from the (phi) transformation zeroes out, and I am left with scalar flux.
My question is this:
I know that rho is the floating point, but the B field I am using is not the same for all values of rho, correct? It varies from (b-a) to (b+a) ?
Do I integrate across rho from (b-a) to (b+a) ?? or has this difference already been accounted for?
Should I be integrating across different form of B rather than just using the generic form from the infinite wire??
and if so, do I do this before I take the dot product?
It seems that rho is only dependent on an x coordinate because of the infinite wire, and not a z coordinate, so would there still a transformation of rho to cartesian for this integral?
I am stuck here, any help varying this rho would be greatly appreciated.
Thanks