Help with Calc 3 problem!?

Experiments show that a steady current I in a long wire produces a magnetic field B that is tangent to any circle in the plane perpendicular to the wire and whose center is the axis of the wire. Ampere's Law relates the electric current to its magnetic effects and states that

∫B (dot) dr = (mu naught) * I

where I is the net current that passes through any surface bounded by a closed curve C and mu naught is a constant called the permeability of free space. By taking C to be a circle with radius r, show that the magnitude B= |B| of the magnetic field at a distance r from the center of the wire is

B= ((mu naught) * I) / (2 pi r)

I've tried a few methods, but they've amounted to nothing. I'm having trouble identifying B or dr.

Really I just have no idea how to start

Could someone maybe give me a push?

Thanks!

1 Answer

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  • freeed
    Lv 5
    8 years ago
    Favorite Answer

    The integral is around the closed curve C which has circumference 2(pi)r - the sum of the differential lengths. B is what we'll find after performing the integration and isolating the result:

    Int[Bdr] = B{Int(dr)} = B{2(pi)r = (mu naught) => B = (mu naught)I/[2(pi)r]

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