Q. 435.0( 1 Vote )

A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the center becomes zero?

Answer :

For the magnetic field at the center to be zero, the magnetic field due to the circular loop has to be exactly equal and opposite to the long straight wire at the center.


Given:


Current carried by circular loop of radius r = i


Current carried by long straight wire = 4i


Formula used:


Magnetic field at the center of a circular loop due to current in the loop(Bl) = , which points into the plane of the paper.


Here


μ0 = magnetic permeability of vacuum,


i = current carried by the loop,


r = radius of the loop


Magnetic field due to an infinitely long wire at a distance x from it(Bw) = , which points out of the plane of the paper.


Here


μ0 = magnetic permeability of vacuum,


i = current carried by the wire,


x = distance of the center of the circle from the wire


Hence, from given information,


, and


where Bl = magnetic field due to loop, Bw = magnetic field due to wire, r = radius of loop, x = distance of the center of the circle from the wire


Hence, for the magnetic field at the center to be 0,



=> =>


Hence, for the magnetic field to be 0, the wire has to be placed at a distance of 4r/π from the center of the circular loop. (Answer)


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