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