Two long, straight wires, one above the other, are seperated by a distance 2a an

Question

Two long, straight wires, one above the other, are seperated by a distance 2a and are parallel to the x-axis. Let the + y-axis be in the plane of the wires in the direction from the lower wire to the upper wire. Each wire carries current I in the + x-direction. Find B - the net magnetic field of the two wires at the following points in the plane of the wires.



A) Midway between the wires. (Express your answer in terms of the variables I, a, and appropriate constants (mu_0 and pi). Enter your answers in the format B(x), B(y), B(z), separated by commas.


B) At a distance a above the upper wire. (Express your answer in same format as above)


C) At a distance a below the lower wire. (Express your answer in same format as above)

Explanation / Answer

part (a) is quite easy actually. Just use the right hand rule. Point your thumb in the direction of the current and see the way your fingers curl. Do this for both wires and you will see that the fields point in opposite directions between the wires. For equal currents I, the fields are equal and opposite and cancel out. For parts (b) and (c), the magnitudes of the fields will be the same but opposite directions. Just add the contributions of the fields due to each wire individually at a distance a for one wire and a distance of 3a for the other one.

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