The figure below shows two long straight wires in the xy pla

The figure below shows two long, straight wires in the xy plane and parallel to the x axis. One wire is at y = 6.0 cm and the other wire is at y = +6.0 cm. The current in each wire is 10 A. If the currents are both in the x direction, find the magnetic field at the following points on the y axis.

Solution

Since B = u₀I/(2piR) at a distance R from a straight wire carrying a current I.
For the upper wire, the magnetic field points out of the xy-plane. For the lower wire it points into the xy-plane. Hence the fields tend to cancel.

Denoting into the plane as positive, we have

a. B = u0/(2 pi) * 10 A * ( 1/(0.034 m) - 1/ (0.086 m) )
b. B = u0/(2 pi) * 10 A * ( 1/(0.06 m ) - 1/ (0.06 m) ) (the negative of a)
c. B = u0/(2 pi) * 10 A * ( 1/(0.086 m ) - (1/(0.034m) )
d. B = u0/(2 pi) * 10 A * ( 1/(0.138 m ) - (1/(- 0.018m) )
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