Two long, parallel wires carry current in the x-y plane. One wire carries 30 A to the left along the x-axis. The other carries 50 A to the right along a parallel line at y = 0.28 m. At what y-axis position in meters is the magnetic field equal to zero?
I saw that how Elena doing, but when I tried it was wrong. She found that 0.105. At first, I was also tried in same way. It was wrong.. any other information pls?
To find the y-axis position where the magnetic field is equal to zero, we can use the concept of the magnetic field produced by a current-carrying wire. The magnetic field at a point due to a current-carrying wire is given by the right-hand rule and is proportional to the current and inversely proportional to the distance from the wire.
In this case, we have two parallel wires, one carrying a current of 30 A to the left along the x-axis and the other carrying a current of 50 A to the right at y = 0.28 m.
To find the y-axis position where the magnetic field is zero, we need to calculate the magnetic field produced by both wires at various y-axis positions and find where they cancel out.
Let's say we choose a y-axis position "y" and consider the magnetic field produced by the wire carrying 30 A. This wire is located at x = 0. The magnetic field due to this wire can be calculated using the formula:
B1 = (μ₀ * I1) / (2πr₁)
where B1 is the magnetic field, μ₀ is the permeability of free space (4π * 10⁻⁷ T·m/A), I1 is the current in the wire (30 A), and r₁ is the distance from the wire (which is equal to y in this case).
Similarly, we can calculate the magnetic field produced by the wire carrying 50 A at y = 0.28 m, which is located at a distance x = y * tan(θ), where θ is the angle between the y-axis and the parallel line along which the wire is carrying the current. Since both lines are parallel, θ = 0, and x = 0. Therefore, the magnetic field due to this wire can be calculated using the same formula as above, with I2 = 50 A and r₂ = y.
Now, at any y-axis position, the magnetic field due to the wire carrying 30 A is directed to the left, and the magnetic field due to the wire carrying 50 A is directed to the right. For the magnetic field to be zero at that position, the magnitudes of these two fields must be equal.
Therefore, we need to solve the equation:
B1 = B2
(μ₀ * I1) / (2πr₁) = (μ₀ * I2) / (2πr₂)
30 / (2πy) = 50 / (2πy)
Cross-multiplying:
30y = 50y
Simplifying:
20y = 0
Since y cannot be zero (as it represents a position on the y-axis), this equation has no solution, which means there is no y-axis position where the magnetic field is equal to zero.
Hence, the magnetic field is never zero along the y-axis in this scenario.