Joining two wires, magnetic fields and a little algebra

AI Thread Summary
To find the magnetic field strength on the line joining two wires with currents flowing, the equation B = μ iD / π(D² − d²) can be derived. This involves summing the contributions of the magnetic fields from both wires at a point a distance d from the midpoint O. A relevant trigonometric identity, (D² − d²) = (D + d)(D - d), is useful in simplifying the calculations. The standard formula for the magnetic field due to a long straight wire, B = μ i / 2π d, serves as a foundational reference. The discussion highlights the need for clarity in applying these concepts to solve the problem effectively.
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Homework Statement


Consider a general point on the line joining the two wires and a distance d
away from the mid-point O. By summing the magnetic field due to currents of magnitude i flowing in both the wires which are non-zero, show that on the line joining the two wires, the magnetic field strength is given by:

B= μ iD / π(D2 −d2)

Homework Equations


(D^2 −d^2) = (D+d)(D-d) ****** a simple trig identity
B= μ i / 2π d

The Attempt at a Solution


I'm kinda stuck - any pointers on where to start?
 
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Just bumping it back up - anyone any ideas?
 

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