A long circular pipe with outside radius R carries a (uniformly distributed) cur

Question

A long circular pipe with outside radius R carries a (uniformly distributed) current i = 10 A into the page as shown in the figure. A wire runs parallel to the pipe at a distance 3R from center to center. Find the magnitude and direction of the current in the wire such that the resultant magnetic field at point P between them and a distance R from the wire has the same magnitude as the resultant field at the center of the pipe but is in the opposite direction. Take positive current as into the page and negative as out of the page.

Explanation / Answer

Bp = -Bc

but

Bp wire > -Bc wire

Bc = 0 iwire / 2r

=  0 iwire / 2(3R)

Bp = Bpipe-Bwire

= 0 i pipe / 2(2R) - 0 iwire / 2(3R)

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