Question

A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at x=−2.0cm . A second, parallel wire carrying a 3.5 A current intersects the x-axis at x=+2.0cm

At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

Answer 1

if the two currents are in the same direction, magnetic field will be zero somewhere in between the wires

now let it be at x = a cm

then u_o5/(2pi x (2+a)) = u_o3.5/(2pi x (2-a))

=> 5(2-a) = 3.5(2+a)

=> 10 - 5a = 7 + 3.5a

=> 3 = 8.5a => a = 3/8.5 = 0.35294 cm

if the two currents are in opposite directions then it will be zero somewhere on x > 2cm, let at x = b cm

then u_o5/(2pi x (2+b)) = u_o3.5/(2pi x (b-2))

5(b-2) = 3.5(2+b)

1.5b = 17 => b = 11.3333 cm