This seems a simple question but I'm not able to understand it properly. Say we have two parallel wires carrying same current I in different directions. We need to calculate the magnetic field at any point on the wires plane (not between the wires).
We know that the magnetic field (H) from one wire is I/2*pi*r where r is the distance from the wire. We can then use superposition to find the total magnetic field from both wires. The magnetic fields will tend to cancel each other but the net field will NOT be zero because the wires are not at the same distance from the test point.
Now, if we try to apply Ampere's law along a circular path that encloses both wires, the magnetic field will equal to zero since the current passing through the enclosed surface is zero (since both currents are equal but in opposite directions). Why does this method give us a different answer?
Best Answer
The magnetic field is not 0, but the integral around the contour is. The reason you cannot apply Ampere's law in this case is that the magnetic field is not homogeneous along the circle