Four long, parallel conductors carry equal currents of I = 9.50 A. The current direction of the current is into the page at points A and B and out of the page at C and D. Calculate the magnitude and direction of the magnetic field at point P, located at the center of the square of edge length 0.200 m.
microT
yarrak cevap
To calculate the magnitude and direction of the magnetic field at point P, we can use the formula for the magnetic field produced by a current-carrying wire. The equation is given as:
B = (μ0 * I) / (2 * π * r)
Where:
B is the magnetic field
μ0 is the permeability of free space (4π x 10^-7 T·m/A)
I is the current
r is the distance from the wire
In this case, we have four long, parallel conductors carrying equal currents. Since the currents are equal and flowing in the same direction, the magnetic fields produced by each wire will add up at point P.
First, let's find the distance between the center of the square and one of the wires. The square has an edge length of 0.200 m, and since point P is located at the center, the distance from the center to one of the sides is half of the edge length, which is 0.100 m.
Since there are four conductors, there will be four magnetic fields that contribute to the overall magnetic field at point P. Two of the wires have currents flowing into the page at points A and B, while the other two wires have currents flowing out of the page at points C and D. The magnetic fields produced by the wires with currents flowing into the page will be in the opposite direction compared to the magnetic fields produced by the wires with currents flowing out of the page.
Now, we can calculate the magnetic field produced by each wire. Plugging in the values into the formula, we have:
B1 = (μ0 * I) / (2 * π * r)
B2 = (μ0 * I) / (2 * π * r)
B3 = -(μ0 * I) / (2 * π * r)
B4 = -(μ0 * I) / (2 * π * r)
Since the two wires with currents flowing into the page have the same direction of magnetic field and the two wires with currents flowing out of the page have opposite directions, we can combine them:
B_total = B1 + B2 + B3 + B4
= (μ0 * I) / (2 * π * r) + (μ0 * I) / (2 * π * r) - (μ0 * I) / (2 * π * r) - (μ0 * I) / (2 * π * r)
= 0
After combining the magnetic fields, we find that the overall magnetic field at point P is zero. Therefore, the magnitude of the magnetic field at point P is 0 μT, and its direction is undefined.
Please note that although the individual magnetic fields produced by the wires are not zero, their combination cancels out at point P due to their opposite directions.