Question

# A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at...

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?

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 uo5/(2pi x (2+a)) = uo3.5/(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 uo5/(2pi x (2+b)) = uo3.5/(2pi x (b-2))

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

1.5b = 17 => b = 11.3333 cm

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