Magnetic Field and Parallel Wires

[Skye77]

I have four parallel wires carrying equal currents of 2 amps arranged in a square (see picture attachment for clarification) The figure is an end-view of the wires and each side of the square has an equal length of 0.1m. The direction of current is -Z for A, B, and C; and the direction of current is + Z for D.

How can I determine the magnitude of the magnetic field at point P in the center of the square?

I have the equation F=I'L x B, but I'm not sure how to solve this. Any pointers would be appreciated. Thanks!

 

[jbsteele]

The equation you need to use is the Biot-Savart law: B = (μ₀/4π) * ∫ I x dl x r/r³where μ₀ is the magnetic permeability of free space, I is the current, dl is an infinitesimal element of the conductor, and r is the distance from the source to the point where the field is being calculated.For this problem, you can start by breaking the square into four infinitesimal line segments, one for each wire, and then integrate them. The integral will depend on the angle of the line segment relative to the point P, which can be determined from the geometry of the square. The resulting magnetic field at point P can then be calculated.

 

[tomcue]

I would first like to commend you for your use of the correct equation, F=I'L x B, to determine the magnetic field at point P. This equation is known as the Biot-Savart law and is commonly used to calculate the magnetic field generated by a current-carrying wire.

To solve this equation, you will need to first determine the distance between the wire and point P. In this case, the distance is the same for all wires and is equal to the length of one side of the square, 0.1m.

Next, you will need to calculate the vector cross product, L x B, for each wire. This can be done by taking the cross product of the vector representing the current direction and the vector representing the distance from the wire to point P.

Once you have calculated the individual cross products for each wire, you can then add them together to get the total magnetic field at point P. Remember to pay attention to the direction of the magnetic field, as it will depend on the direction of the current and the direction of the cross product.

Lastly, it is important to note that the magnetic field from each wire will contribute to the overall field at point P, so you will need to take into account the magnetic field from each wire when calculating the total field.

I hope this helps guide you in solving the problem. If you need further assistance, I recommend consulting a textbook or seeking help from a colleague or instructor. Keep up the good work in utilizing scientific equations to solve problems!