Each of two long straight parallel wires separated by a distance of 24.0 cm carries a current of 5.00 A
in the same direction. What is the magnitude of the resulting magnetic field at a point that is 14.0 cm
from each wire?
I have tried (U0I/2pir)2 as well as U0I/4pia(cos(theta) -cos(theta2)) Where theta 1 is approx 30 and theta 2 is approx 150. And a series of other variations which never yield close to the given answers. I would like to know which equation I am supposed to use. Been working on this since for 5 days now.
You will have to draw a sketch first, then note that the two magnetic field will be opposing in a large degree. So break up each magnetic field into a horizontal component (which the add in the same direction), and a vertical, which oppose and cancel. Then compute the sum in each direction.
There is an easier way, once you realize what is happening. Both fields are equal in magnitude, so it is you have to compute only one field in the horizontal component, and double it.
Ul I/2PIr * sinTheta * 2
and Theta = arcCos12/14
Draw the sketch.
To determine the magnitude of the resulting magnetic field at a point between two long parallel wires, you can use the Biot-Savart law. This law states that the magnetic field created by a current-carrying wire at a point is directly proportional to the current and inversely proportional to the distance between the wire and the point.
The formula for the magnitude of the magnetic field created by a wire is given by:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnetic field strength,
μ₀ is the permeability of free space (a constant equal to 4π × 10^ -7 T·m/A),
I is the current flowing through the wire, and
r is the distance from the wire.
In your case, you have two wires carrying a current of 5.00 A, and you want to find the magnetic field at a point 14.0 cm (0.14 m) from each wire. Since the wires are parallel, the magnetic fields produced by each wire will add up.
To find the total magnetic field at your desired point, you can add the magnetic fields produced by each wire using the principle of superposition. Remember to account for the fact that the wires are in the same direction.
B_total = B_wire1 + B_wire2
B_wire1 = (μ₀ * I) / (2π * r1)
B_wire2 = (μ₀ * I) / (2π * r2)
Substituting the given values, we can evaluate the magnetic field created by each wire individually:
B_wire1 = (4π × 10^ -7 T·m/A * 5.00 A) / (2π * 0.14 m)
B_wire2 = (4π × 10^ -7 T·m/A * 5.00 A) / (2π * 0.14 m)
Simplifying the equations, we get:
B_wire1 = 0.036 T
B_wire2 = 0.036 T
Finally, we can find the total magnetic field at the point using:
B_total = B_wire1 + B_wire2
B_total = 0.036 T + 0.036 T = 0.072 T
Therefore, the magnitude of the resulting magnetic field at a point that is 14.0 cm from each wire is 0.072 T.