Two long, parallel wires carry current in the x-y plane. One wire carries 30 A to the left along the x-axis. The other carries 50 A to the right along a parallel line at y = 0.28 m. At what y-axis position in meters is the magnetic field equal to zero?

μ₀I₁/2πy= μ₀I₂/2π(0.28-y)

I₁(0.28-y)= I₂y
30(0.28-y)=50y
80y=8.4
y=8.4/80=0.105 m

wrong answer. is there another solution to it? please try again. thanks

To find the y-axis position where the magnetic field is equal to zero, we need to apply Ampere's Law, which states that the magnetic field around a closed loop is directly proportional to the total current passing through the loop.

In this case, we have two long, parallel wires carrying currents in opposite directions. The magnetic field at any point due to the first wire is given by:

B1 = (μ0 * I1) / (2π * r1),

where μ0 is the permeability of free space, I1 is the current in the first wire, and r1 is the distance between the first wire and the point of interest.

Similarly, the magnetic field at any point due to the second wire is given by:

B2 = (μ0 * I2) / (2π * r2),

where I2 is the current in the second wire and r2 is the distance between the second wire and the point of interest.

For the magnetic field to be zero, the fields created by the two wires must cancel each other out. Since the wires are parallel, the distance between them is constant.

Therefore, we can set up the equation:

B1 = B2,

(μ0 * I1) / (2π * r1) = (μ0 * I2) / (2π * r2).

Canceling out common terms and rearranging the equation:

I1 / r1 = I2 / r2.

Substituting the given values, I1 = 30 A, I2 = 50 A, and r1 = 0 (the first wire is on the x-axis), the equation becomes:

30 A / 0 = 50 A / r2.

Since the value of r1 is 0, the magnetic field due to the first wire is always infinite. Therefore, wherever the second wire is, the magnetic field will always be zero.

Thus, the y-axis position where the magnetic field is zero is at y = 0.28 m.