# The Bio-Savart Law applied to a square loop

• georgeh
In summary, the magnetic field at the center of the square is due to the current flowing through the wire and the magnetic field lines created by the triangle you drew.
georgeh
I made a typo. I meant, Biot- Savar Law( sorry ).1. Homework Statement
A conductor in the shape of a square Loop of edge length l= 0.400 m carries a current I = 10.0A. Calculate the magnitude and direction of the magnetic field at the center of the square.

## Homework Equations

db = u_0/(4pi) * I ds x r_units vector /r^2

## The Attempt at a Solution

I know that that I can take out the constants, u_0/4*pi and the I and integrate ds x r_unit vector /r^2
I know also that all four sides create a magnetic field B into the page. I just don't know how to state my r. I also know that
db = k* ds sin(thetha) /R^2
( with all the constatnts factored out, k = all the constants), but I am not sure how thetha varies, i am assuming r would be l/2 if we draw our axis at the point p. but i am not sure how thetha varies.. nor ds. any help would be appreciated.

Last edited:
RE: theta

Draw a triangle using one side of the square and the center of the square. What kind of triangle is this? How does your angle theta relate to this triangle?

If by r you mean the distance from a bit of the wire dl to the point where you are calculating the field at the center of the loop, it is a function of the angle between the wire and a line from the wire to the center of the loop. It may be L/2 somewhere, but certainly not everywhere.

I get a 45-45-90 triangle. if i draw a perpendicular bisector from pt P to the wire, and draw an r at an angle thetha to the point P..

georgeh said:
I get a 45-45-90 triangle. if i draw a perpendicular bisector from pt P to the wire, and draw an r at an angle thetha to the point P..

You also get a 45-45-90 if you draw from point P to two ends of one side. The lengths of those two lines are the intial and final values of r in the integral for one side. r gets shorter and then longer again as you move from one end of the wire to the other. The angle between dl and r starts at 45 degrees and increases as you move from end to end. How big does it get? Can you find a relationship between this angle, the distance from one end to a point on the wire and r from this point to the center of the loop? You might find it helpful to think about the relationship between the sine of an angle and the sine of the supplementary angle.

## 1. What is the Bio-Savart Law?

The Bio-Savart Law is a mathematical equation that describes the magnetic field produced by a current-carrying wire or a group of current-carrying wires. It is named after French physicist Jean-Baptiste Biot and French mathematician Felix Savart.

## 2. How is the Bio-Savart Law applied to a square loop?

The Bio-Savart Law can be applied to a square loop by breaking the loop into smaller segments and calculating the magnetic field produced by each segment. Then, the magnetic fields from all the segments are added together to determine the total magnetic field at a specific point.

## 3. What are the variables in the Bio-Savart Law equation?

The variables in the Bio-Savart Law equation include the current (I), the distance from the wire (r), the angle between the wire and the point of interest (θ), and the permeability of free space (μ0). The equation also includes a constant, k, which depends on the shape of the current-carrying wire or loop.

## 4. What is the significance of a square loop in the application of the Bio-Savart Law?

A square loop is often used in the application of the Bio-Savart Law because it is a simpler and more symmetric shape compared to other types of loops. This allows for easier calculations and a better understanding of the behavior of magnetic fields in a loop.

## 5. Can the Bio-Savart Law be used to calculate the magnetic field at any point?

Yes, the Bio-Savart Law can be used to calculate the magnetic field at any point in space as long as the current-carrying wire or loop is known. This allows for the prediction and understanding of the behavior of magnetic fields in various situations, making it a fundamental equation in electromagnetism.

• Introductory Physics Homework Help
Replies
10
Views
299
• Introductory Physics Homework Help
Replies
4
Views
229
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
18
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
430
• Introductory Physics Homework Help
Replies
5
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
8K
• Introductory Physics Homework Help
Replies
30
Views
832
• Introductory Physics Homework Help
Replies
21
Views
2K