Answer to Question #163850 in Electricity and Magnetism for bibo

Question

Shown in the figure, in cross-section, are several conductors that carry currents through the plane of the figure. The currents have the magnitudes I₁ = 4.0A, I₂ = 6.0A and I₃ = 2.0A and the directions shown. Four paths, labeled a through d, are shown.

1. What is the line integral for each path (a, b, c, d)? Each integral involves going around the path in the counterclockwise direction.
2. What will happen to the line integrals if we go around the path in the clockwise direction?

Answer 1

Answer

According to physics concepts

line integral is given

$\int B.dl=\mu_0I_{net}$

Along path (a) $I_{net}$ ​ current enclosed by this path is zero.Hence line integral =0Along path

(b)$I_{net}$ ​ is into the plane of the paper. 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.