Question

Each of the eight conductors in the figure carries 1.61 A of current into or out of the page. Two paths are indicated for the line integral B middot d s, what is the value of the integral for (a) path 1 and (b) path 2?

Answer 1

The path integral along a circle centered around the wire (see Figure 31.1) is equal to

where I is total current passing through loop

path

Let I be +ve when into the plane, and -ve when out of the plane

a) integral₁ = u₀(-2I+I) = -u₀I = -20.22*10^-7 = -2.02*10^-6

b) integral₁ = u₀(-2I+2I) = 0