Question

A long wire carrying a 5.5 A current perpendicular to the xy-plane intersects the x-axis atx=−2.0cm. A second, parallel wire carrying a 2.5 A current intersects the x-axis atx=+2.0cm.

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

Answer 1

The point on the x-axis where the magnetic field is zero when the two currents are in the same direction is at x = -2.0 cm. When the two currents are in opposite directions, the magnetic field is zero at x = -0.77 cm.

Step-by-step explanation:

To find the point on the x-axis where the magnetic field is zero when the two currents are in the same direction, we can use the formula for the magnetic field generated by a straight wire:

B = μ0I/2πr

So for the first wire with a current of 5.5 A, we have B1 = (μ0*5.5)/(2π*0.02) = 0.087 T. And for the second wire with a current of 2.5 A, we have B2 = (μ0*2.5)/(2π*0.02) = 0.040 T.

Since the two currents are in the same direction, the magnetic fields will add up. Therefore, the magnetic field at the point where they intersect on the x-axis will be the sum of B1 and B2. So:

B = B1 + B2 = 0.087 + 0.040 = 0.127 T

So the point on the x-axis where the magnetic field is zero when the two currents are in the same direction is at x = -2.0 cm.

When the two currents are in opposite directions, the magnetic fields will subtract from each other. So the point on the x-axis where the magnetic field is zero is the point where the magnetic fields due to the two currents cancel each other out:

B = B1 - B2 = 0.087 - 0.040 = 0.047 T

So the point on the x-axis where the magnetic field is zero when the two currents are in opposite directions is at x = -0.77 cm.