Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. At what point between the two wires are the contributions from the two wires the same?
A) 0.040 m from the 20 A wire
B) 0.080 m from the 20 A wire
C) 0.12 m from the 20 A wire
D) 0.16 m from the 20 A wire
E) 0.18 m from the 20 A wire

Question

Quizplus · Accepted Answer

We can use the equation for the magnetic field produced by a long, straight wire:

B = (μ0/2π) * (I/r)

Where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

At the point between the two wires where the contributions are equal, the magnetic field produced by the 20 A wire will be equal in magnitude but opposite in direction to the magnetic field produced by the 5.0 A wire. So:

(μ0/2π) * (20/0.16) = (μ0/2π) * (5.0/x)

Solving for x gives:

x = (5.0 * 0.16) / 20 = 0.04 m

So the point where the contributions are equal is 0.04 m from the 20 A wire, which is answer choice D.

Two Long Parallel Wires Carry Currents of 20 a and 5.0