Question

Let a filamentary current of 5 mA be directed from infinity to the origin on the positive z axis and then back out to infinity on the positive x axis. Find H at P(0,1,0).

Answer 1

I am solving the problem using Biot Savart Law.

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Since you want the magnetic field at (0,1,0), this is a point exactly 1 meter (I assume the coordinates are measured in meters)along the y axis from the point (0,0,0)

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At this point, there are two "semi infinite" currents... onecoming in from the z axis and one going out along the x axis. The magnitude field from a semi infinite current is given by the Biot Savart law:

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     H = k I /r          where   k = 1 x 10^-7

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The current along the z axis creates a mag field in the x direction of magnitude...

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           1 x 10^-7 * 5 x 10^-3 / 1   = 5 x 10^-10  

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And the current along the x axis creates a mag field of the same magnitude in the x direction.

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So the total magnetic field is given by

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    H =   (1, 0, 1)      in x10^-6Tesla or    microTesla