Question

The figure below shows, in cross section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes I₁ = 2.0 A, I₂ = 5.0 A, and I₃ = 2.6 A. and the directions shown. Four paths, labeled a through d, are shown. What is the line integral ·dl for each paths? Each integral involves going around the path in the counterclockwise direction.

Answer 1

Path a)

No current is inside that path, thus line integral equals 0 Tm

Path b)

$\oint$ B.dl=u0.I enclosed

=4x3.14x10^-7x2

=2.512x10^-6Tm

Path c)

$\oint$ B.dl=u0(-I1+I2)

=4x3.14x10^-7x(3)

=3.768x10^-6 Tm

Path d)

$\oint$ B.dl=u0(-I1+I2+I3)

=4x3.14x10^-7x(5.6)

=7.03x10^-6 Tm