Magnetic vector potential for antiparallel currents

[teastation]

Two infinitely long wires separated by distance d. Currents: I1 = -I2. Find potential vector as a function of r1 and r2 at a point P (r1 and r2 distances to P from wire one and wire two).
Del cross A= B
B = (mu I)/(2pi r)



Using Ampere's, I get an expression for the magnetic field that involves two different distances, r1and r2. I see that integrating this expression with respect to distance will give me the vector potential. But with two distances to take into account, I don't know how to solve this.

 

[teastation]

Oh I'm using cylindrical coordinates. With the wires oriented along the z axis, the only term that survives del cross A is the azimuthal component.
-partial dA/ds = (mu I)/2pi [(1/r1) - (1/r2)] in the phi direction.

 

[TSny]

Hello.

Can you find an expression for A for a single infinitely long straight wire carrying current I ? If so, then the superposition principle will get you the answer fairly easily.

 

[teastation]

Thanks TSny. Duh... the problem asks me to get the vector as a function of two different distances. I don't need to find a way to relate them. QuiteEasilyDone