Question

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?

Answer 1

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