- #1
aim1732
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Are magnetic field lines around a finite current carrying straight conductor concentric circles in plane perpendicular to length of wire? I have seen texts derive an expression for it :
B = μ0.i/4πd [cos Φ1-cosΦ2]
where d is perpendicular distance of separation of the point from the wire and Φ1 and Φ2 are angles the end points of the wire subtend at the point.
Clearly all points at distance d from the wire have equal field magnitude, in direction perpendicular to the plane containing the wire and the point.
This is from Biot Savart Law.
The reason I doubt this is that if we imagine an Amperian loop along one of these circular field lines and calculate the line integral of B.dl it does not give me μ0.i. This procedure works well for infinitely long conductors---- I know that is a symmetrical situation suited for Ampere's Law but I see nothing different for finite conductors. According to the equation I wrote above field lines for finite conductors are identical to those for infinite conductors.
I am guessing I am missing something obvious. I would rather have someone tell me how symmetry manifests in Ampere's Law as against Gauss's Law-it was much simpler for Gauss's Law I guess.
All comments are welcome.
B = μ0.i/4πd [cos Φ1-cosΦ2]
where d is perpendicular distance of separation of the point from the wire and Φ1 and Φ2 are angles the end points of the wire subtend at the point.
Clearly all points at distance d from the wire have equal field magnitude, in direction perpendicular to the plane containing the wire and the point.
This is from Biot Savart Law.
The reason I doubt this is that if we imagine an Amperian loop along one of these circular field lines and calculate the line integral of B.dl it does not give me μ0.i. This procedure works well for infinitely long conductors---- I know that is a symmetrical situation suited for Ampere's Law but I see nothing different for finite conductors. According to the equation I wrote above field lines for finite conductors are identical to those for infinite conductors.
I am guessing I am missing something obvious. I would rather have someone tell me how symmetry manifests in Ampere's Law as against Gauss's Law-it was much simpler for Gauss's Law I guess.
All comments are welcome.