Magnetic Field given two wires

[jamesbiomed]

Homework Statement

A long pair of insulated wires serves to conduct 29 A of dc current to and from an instrument.

(a) If the wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10 cm from their midpoint, in their plane (see figure)?


http://www.webassign.net/gianpse3/28-31.gif

Homework Equations

B = µ0*I/(2*π) * (1/r1 - 1/r2).

µ0 = 4*π*10^-7 T*m/A

B = 2*10^-7*I*(1/r1 - 1/r2)

r1 = .0986 m
r2 = .1014 m

The Attempt at a Solution

The equations above are the correct method for solving this, its from yahoo answers. My question is about the values for r. They add up to .2, which I'm guessing is because the current is going in opposite directions. But I do not understand why they are not the same, given that all the dimensions are identical.

Thanks in advance...

 

[anathema]

Thank you for your question. The reason why the values for r1 and r2 are not the same is because they are measuring the distance from the midpoint of the wires to the point where you are calculating the magnetic field. Since the wires are 2.8 mm apart, you need to consider the distance to each wire separately.

For example, if you are calculating the magnetic field at a point 10 cm from the midpoint, r1 would be the distance from the midpoint to the first wire (which is 2.8 mm/2 = 1.4 mm), plus the distance from the first wire to the point where you are calculating (10 cm), giving a total distance of 10.0014 cm. Similarly, r2 would be the distance from the midpoint to the second wire (2.8 mm/2 = 1.4 mm), plus the distance from the second wire to the point where you are calculating (10 cm), giving a total distance of 10.0014 cm.

I hope this helps clarify the issue. Please let me know if you have any further questions.

Scientist