Two long, parallel, current-carrying wires lie in an xy-plane. The first wire lies on the line y = 0.310 m and carries a current of 25.5 A in the +x direction. The second wire lies along the x-axis. The wires exert attractive forces on each other, and the force per unit length on each wire is 300 µN/m. What is the y-value (in m) of the line in the xy-plane where the total magnetic field is zero?
i1 = current in the wire lying at the origin = ?
i2 = current in the wire at y = 0.310 m , = 25.5 A
r = distance between the two wires = 0.310 m
F = force per unit length between the wire = 300 x 10-6 N/m
force per unit length between two current carrying wires is given as
F = (/4) (2 i1 i2/r)
300 x 10-6 = (10-7) (2 i1 (25.5)/0.310)
i1 = 18.24 A
let the magnetic field is zero at distance "d" from the wire at origin
for the magnetic field to be zero
magnetic field by wire at origin = magnetic field by wire at y = 0.310
(/4) (2 i1/d) = (/4) (2 i2/(r - d))
((18.24)/d) = ((25.5)/(0.310 - d))
d = 0.13 m
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