Question

A long straight wire carries 5A out along the positive X-axis and a second wire carries 7A out along the positive Y-axis. Find their combined field at the point X=4cm and Y=6cm

Answer 1

$B_i=\frac{\mu_0 I_i}{2\pi d_i},$

$B=\sqrt{B_x^2+B_y^2},$

$B_x=\frac{\mu_0 I_x}{2\pi y},$

$B_y=\frac{\mu_0 I_y}{2\pi x},$

$B=\frac{\mu_0}{2\pi}\sqrt{\frac{I_x^2}{y^2}+\frac{I_y^2}{x^2}}=3.88\cdot 10^{-5}~T.$