Two long parallel wires carry unequal currents in opposite directions. The ratio of the currents is 3 to 1. The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT. What is the larger of the two currents?
A) 0.5 A
B) 1.0 A
C) 1.5 A
D) 2.0 A
E) 3.0 A

Question

Quizplus · Accepted Answer

Let the smaller current be I and the larger current be 3I.
Using the formula for the magnetic field due to a straight conductor: B = μ0(I/2πr), we can find the value of the currents as follows:
4.0 μT = μ0(I/2π(0.1m)) - μ0(3I/2π(0.1m))
4.0 μT = μ0(I/0.628) - μ0(3I/0.628)
4.0 μT = μ0(I/0.628) - 3μ0(I/0.628)
4.0 μT = -2μ0(I/0.628)
I = -3.156 A
Since the ratio of the currents is 3 to 1, the larger current is 3I = -9.468 A. However, we need to take the absolute value of these currents since negative current doesn't make physical sense. Therefore, the larger current is approximately 1.5 A (choice C).

Two Long Parallel Wires Carry Unequal Currents in Opposite Directions