Two long parallel wires 10.0 cm apart carry currents of 3.0 A and 2.9 A in the same direction.Is there any point between the two wires where the magnetic field is zero?

Question

Quizplus · Accepted Answer

The magnetic field created by a current-carrying wire decreases as the distance from the wire increases following inverse proportionality to the distance. At a point between two parallel wires, the magnetic field due to one wire is directly proportional to its current and inversely proportional to the distance from it, and the magnetic field due to the other wire is directly proportional to its current and inversely proportional to the distance from it, but in the opposite direction. Therefore, to find the point where the magnetic field is zero, we need to equate the magnetic field due to the two wires and solve for the distance.

Let the distance from the 3.0-A wire be x, then the distance from the 2.9-A wire is 10.0 - x. The magnetic field due to the 3.0-A wire at the point is:

B1 = μ0I1/2πx

The magnetic field due to the 2.9-A wire at the point is:

B2 = μ0I2/2π(10.0 - x)

Equating B1 and B2 and solving for x, we get:

x = (μ0I2/μ0I1 + I2) × 10.0 = (2.9/(3.0 + 2.9)) × 10.0 ≈ 5.1 cm

Therefore, the magnetic field is zero at a point 5.1 cm from the 3.0-A wire and 4.9 cm from the 2.9-A wire.

Two Long Parallel Wires 10