Question

A long wire carrying a 4.0 A current perpendicular to the xy-plane intersects the x-axis at x=−2.2cm. A second, parallel wire carrying a 2.8 A current intersects the x-axis at x=+2.2cm

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

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

Answer 1

let

I1 = 4 A

I2 = 2.8 A

A) when the two currents are in the same direction, in between the wires the magnetic field direction are opposite to each other.

let at x cm from Origin Bnet = 0

B1 = B2

mue*I1/(2*pi*(2.2+x)) = mue*I2/(2*pi*(2.2-x))

4/(2.2+x) = 2.8/(2.2 - x)

x = 0.39 cm

B) A) when the two currents are in the opposite direction, in between the wires the magnetic field direction is in the same direction.

so, the point where Bnet is zero will be beyond +2.2 cm

let at x cm from Origin Bnet = 0

B1 = B2

mue*I1/(2*pi*(2.2+x)) = mue*I2/(2*pi*(x-2.2))

4/(2.2+x) = 2.8/(x-2.2)

x = 12.5 cm (on rounding 12 cm)