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What is the magnitude and direction of the magnetic field due to straight current carrying wire on that wire? In the uploaded image, two wires are at right angles in a plane carry equal currents. At what points in the plane is the magnetic field zero?
Asked by arjunsah797 | 24 Jan, 2022, 04:14: PM
Let the two current carrying wire be respectively in x-axis and y-axis of cartesian coordinate system.

Current flows in +ve x-axis direection in the wire that is placed on x-axis.

Current flows in -ve y-axis direction in the other wire that is placed y-axis.

Directions of magnetic field for both the wires in all four quadrants are shown in figure.

It can be seen that second and fourth quadrants have magnetic fields in opposite direction .

if currents are equal, then magntiude of magnetic field at a point depends on the perpendicular distance from the point to wire.

Hence the blue line AB that subtends 45o with the axes have equi-distant points from axes .

Hence along the blue line AB , magnetic fields due to both the wire cancel each other .

Hence along the blue line AB, we have zero magnetic field.
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