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Hi there I am just really confused as to how they arrived at the answer to this problem. I attached a picture of the entire question and the solution.
Please see attached file.
Biot Savart Law for Magnetism of a Wire where the length of wire is much larger than distance away from the wire where the B field is being measured is:
(μ/4π)(2I/r)
I: current
r: distance from wire
How I approached the problem, I modeled each side of the square of length L as an individual wire such that each wire contributes a B field at the center of the square. Since each side is of length L. I calculated (using a right triangle) that 2L^2= D^2 where D^2 equals the length from corner to corner. So
Solving for D, D = (2L^2)^(1/2) = L(2)^(1/2). Since I want to locate the center I then divided this by 2.
So I figured that the center is located at [L sqrt(2)]/2
I simply then plugged this into the equation above for r. And then multiplied by 4 since there are four wires contributing a magnetic field B at that location.
My final answer: 4(μ/π)(I/(L sqrt(2)) but the answer is actually [(μ)(I)/(2πL)](sqrt(2))
In the explanation they give then end up doing some really complicated math and integrating the general Biot Savart Law to get their answer. Im confused as to why they would integrate. Are they integrating because each section of each of the wires (ΔL) is contributing a magnetic field at B? Why cant I simply use the equation that I used? I feel like a lot of the times I struggle with these problems because I do not know when to use the formula and when to integrate. This is an example of this. Please help me!
Thank you
Homework Statement
Please see attached file.
Homework Equations
Biot Savart Law for Magnetism of a Wire where the length of wire is much larger than distance away from the wire where the B field is being measured is:
(μ/4π)(2I/r)
I: current
r: distance from wire
The Attempt at a Solution
How I approached the problem, I modeled each side of the square of length L as an individual wire such that each wire contributes a B field at the center of the square. Since each side is of length L. I calculated (using a right triangle) that 2L^2= D^2 where D^2 equals the length from corner to corner. So
Solving for D, D = (2L^2)^(1/2) = L(2)^(1/2). Since I want to locate the center I then divided this by 2.
So I figured that the center is located at [L sqrt(2)]/2
I simply then plugged this into the equation above for r. And then multiplied by 4 since there are four wires contributing a magnetic field B at that location.
My final answer: 4(μ/π)(I/(L sqrt(2)) but the answer is actually [(μ)(I)/(2πL)](sqrt(2))
In the explanation they give then end up doing some really complicated math and integrating the general Biot Savart Law to get their answer. Im confused as to why they would integrate. Are they integrating because each section of each of the wires (ΔL) is contributing a magnetic field at B? Why cant I simply use the equation that I used? I feel like a lot of the times I struggle with these problems because I do not know when to use the formula and when to integrate. This is an example of this. Please help me!
Thank you
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