A long wire carrying a 60 A current perpendicular to the xyp

A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects the x-axis at x=2.0cm . A second, parallel wire carrying a 2.0 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 opposite directions?

Solution

Let I1 = 6 A (going into the page)

I2 = 2 A (coming out of the page)

here, I2 < I1

so, the point where net magnetic field is zero is close to I2.

let x is the distance from I2 where net magnetic field is zero.

B2 = B1

mue*I2/(2*pi*x) = mue*I1/(2*pi*(4+x))

I2/x = I1/(4+x)

(4+x)*I2 = x*I1

(4+x)*2 = x*6

8 + 2*x = 6*x

8 = 4*x

x = 2 cm

so, at x = 2 + 2

= 4 cm net magnetic field becomes zero .