# Problems in Magnetism Induced by Current

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##### Solution Summary

We solve several problems regarding the magnetic field induced by various current distributions.

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1. To calculate the magnetic field (flux density) at a given point p due to a portion of wire with given current I, we apply the Biot-Savart law, which says

B(p) = mu0 I/(4 pi) integral((dl X r)/|r^3|),

where dl is a vector portion of the wire pointing in the direction of the current and r is a vector pointing from the portion of wire to p. For the given problem, we first create a coordinate system centered at p and with the x-axis going to the right, the y-axis going up, and the z-axis coming out of the page. Then for the wire on the left, we have

I1 = 5 A

dl_1 = -dy j

r1 = d1 i + yj,

where d1 = 0.03 m is the distance from the wire to P. Thus we have

dl_1 ...

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