- #1

Gene Naden

- 321

- 64

## Homework Statement

Two long, parallel copper wires of diameter 2.5 mm carry currents of 10 A in opposite directions. Assuming that their central axes are 20 mm apart, calculate the magnetic flux per meter of wire that exists between those axes. What fraction of this flux lies inside the wires?

## Homework Equations

Inside a wire, ##B=\frac{\mu_0 i}{i R^2}r##.

Outside a wire, ##B=\frac{\mu_0i}{2\pi r}## where R is the radius of the wire and r is the distance from the center of the wire.

## The Attempt at a Solution

##\Phi_1=2\int _{0}^{R} \frac{\mu_0 i x}{2\pi R^2} dx=\frac{\mu_0 i}{2\pi}##

where x is the vertical distance downward from the center of the wire.

##\Phi_2=2\int_{R}^{s}\frac{mu_0 i}{2\pi r} dr=\frac{\mu_0 i}{2\pi} ln(\frac{s}{R})##

where r is the vertical distance downward from the center of the wire and s is the separation.

##\Phi=\Phi_1+\Phi_2=13.09\mu W/m##

##Frac=\frac{\Phi_1}{\Phi_1+\Phi_2}=15.3 \:percent##

For the flux, I agree with the textbook (Halliday, Resnick & Walker Fundamentals of Physics 5th edition, chapter 31, problem 23). But I disagree for the fraction of flux inside the wire. They get 17%. Can anyone verify my answer or point out where I went wrong?