Figure shows, in cross-section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes `i_1=4.0A, I_2=6.0A`, and `I_3=2.0` A, in the directions shown. Four paths labelled a to d, are shown. What is the line integral `intB. dI` for each path? Each integral involves going around the path in the counter-clockwise direction.

Explanation

`intB.I=mu(i_("net"))`
Along path as net current enclosed by this path is zer.
Hence line integral =0
along path b `i_("net") is `(ox)`. So, magnetic lines along this current is clockwise. But, we have to take line integral in counter clockwise direction. Hence, line integral will be negative.