- #1

ikentrovik

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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. I am 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 can't 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. I am 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 can't 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