Where Do Magnetic Fields Cancel Out in Intersecting Wires?

[doggy physics]

Two very long fixed wires cross each other perpendicularly. They remain infinitely close together but do not touch and remain electrically isolated from each other. Equal currecnts flow in each wire. Indicate the locus of points in the plane containing the wires where the net magnetic field is zero. Justify your answer.

 

[sokratesla]

# Hi,
# To solve this question, you should learn what kind of a magnetic field a current flowing in an infinitely long wire creates. The field due to two wires is just the superposition of itself.
# Draw crossing lines from top view. For both lines indicate whether the field is into the paper or out of the paper on its left side and right side.
# I hope these may help you.

 

[Moetasim]

The net magnetic field will be zero at all points along the line where the two wires intersect. This is because at these points, the magnetic field created by one wire will be cancelled out by the magnetic field created by the other wire. This is known as the "right-hand rule" in electromagnetism, where the direction of the magnetic field created by a current-carrying wire is perpendicular to the direction of the current and the direction of the magnetic field created by the other wire. Since the wires are infinitely close together and have equal currents flowing in opposite directions, the magnetic fields created by them will cancel out at all points along the intersection line. This is a fundamental property of perpendicular magnetic fields and is crucial in many applications, such as in MRI machines and particle accelerators.