Two long parallel wires carry currents of $20 \mathrm {~A}$ and $5.0 \mathrm {~A}$ in opposite directions. The wires are separated by $20 \mathrm {~cm}$. At what point between the two wires do they produce the same strength magnetic field?
A) $16 \mathrm {~cm}$ from the $20 \mathrm {~A}$ wire
B) $8.0 \mathrm {~cm}$ from the $20 \mathrm {~A}$ wire
C) $18 \mathrm {~cm}$ from the $20 \mathrm {~A}$ wire
D) $12 \mathrm {~cm}$ from the $20 \mathrm {~A}$ wire
E) $4.0 \mathrm {~cm}$ from the $20 \mathrm {~A}$ wire

Question

Quizplus · Accepted Answer

The magnetic field due to a long straight wire is given by:$$B = \frac{\mu_0 I}{2\pi r}$$where:* $B$ is the magnetic field strength* $\mu_0$ is the permeability of free space* $I$ is the current* $r$ is the distance from the wireIn this problem, we have two wires carrying currents in opposite directions. The magnetic field due to each wire will be in the same direction, so we can add the magnetic fields due to each wire to find the total magnetic field.At a point between the two wires, the magnetic field due to the $20 \mathrm {~A}$ wire will be stronger than the magnetic field due to the $5.0 \mathrm {~A}$ wire. In order for the total magnetic field to be zero, the magnetic field due to the $20 \mathrm {~A}$ wire must be equal to the negative of the magnetic field due to the $5.0 \mathrm {~A}$ wire.This will occur when the point is $16 \mathrm {~cm}$ from the $20 \mathrm {~A}$ wire and $4.0 \mathrm {~cm}$ from the $5.0 \mathrm {~A}$ wire.

Two Long Parallel Wires Carry Currents Of 20 A20 \mathrm {~A}20 A And 5.0 A5.0 \mathrm {~A}5.0 A

Two Long Parallel Wires Carry Currents Of $20 \mathrm {~A}$ And $5.0 \mathrm {~A}$