Question

two long, straight parallel wires carry currents in the positive y direction. wire 1 is at x=0 and carries a 20A current. wire 2 is at x=20cm and caries a 8A current. at what value of x in the plane of the wires is the magnetic field zero, in cm?

Answer 1

at x = 14.3 cm net magnetic field would be ZERO

Step-by-step explanation:

At the position where net magnetic field would be zero

we will say that

`B_1 = B_2`

here we know that

`B_1 = (\mu_0 i_1)/(2\pi r)`

and due to another wire we have

`B_2 = (\mu_0 i_2)/(2\pi (20 - r))`

so here we have

`B_1 = B_2`

`(\mu_0 i_1)/(2\pi r) = (\mu_0 i_2)/(2\pi (20 - r))`

`(20)/(r) = (8)/(20 - r)`

`5(20 - r) = 2r`

`7 r = 100`

`r = 14.3 cm`