Question

What is the magnetic field midway between two parallel conductors carrying same amount of current in the same direction and in the opposite direction?

Answer 1

Case(1) Conductors carrying same direction current $i$.

Magnetic feild $B_1=\frac{{\mu }_{0}i}{2\pi x}$ into the paper at point P midway. Also $B_2=\frac{{\mu }_{0}i}{2\pi x}$ out of the plane at point P.

Net field $B=B_1+B_2$=$\frac{{\mu }_{0}i}{2\pi x}$-$\frac{{\mu }_{0}i}{2\pi x}=0$

Case(2) Current $i$ is in opposite direction.Magnetic feilld at P is,

$B=B_1+B_2=$($\frac{{\mu }_{0}i}{2\pi x}$+$\frac{{\mu }_{0}i}{2\pi x}$) into the plane.

$\left|B\right|=\frac{{\mu }_{0}i}{\pi x}$

where $x=$distance from conductors,at point P.