Two infinitely long, straight wires are parallel and separated by a distance of

Question

Two infinitely long, straight wires are parallel and separated by a distance of 1.25 meters. They carry currents in the same direction. Wire 1 carries four times the current that wire 2 carries. On a line drawn perpendicular to both wires, locate the spot (relative to wire 1) where the net magnetic field is zero. Assume that wire 1 lies to the left of wire 2 and note that there are three regions to consider on this line: to the left of wire 1, between wire 1 and wire 2, and to the right of wire 2.

Explanation / Answer

let curret in wire 2 is I.

current in wire 1 is 4*I.

as current are carried in same direction, the only place where magnetic field will be zero is in between the two wires.

let the point is at a distance of d from wire 1.

then distance from wire 2=1.25-d

field due to a wire carrying current at a distance=mu*current/(2*pi*distance)

where mu=magnetic permeability

hence equating magntiude of magnetic field due to both wires,

mu*4*I/(2*pi*d)=mu*I/(2*pi*(1.25-d))

==>4*(1.25-d)=d

==>5-4*d=d

==>5*d=5

==>d=1

hence at a distance of 1 meters from the wire 1, net magnetic field will be zero.

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