Magnetic Field of rectangular current loop

In summary, the magnetic field of a current loop lying symmetrically on the xy-plane is found using the Biot-Savart law or the derived formula. If someone cannot get their triangles correct, they will need to use the Biot-Savart law to solve for the magnetic field.
  • #1
cconfused
4
0

Homework Statement



Find the magnetic field of a rectangular current loop lying symmetrically on the xy-plane. Find the magnetic field at (0,0,z)

Homework Equations



Biot-Savart law or derived formula (Mu/4*Pi) * sin(theta2)-sin(theta1)/s

The Attempt at a Solution


I am NOT good with getting my trianges correctly. I know that B1=B3 and B2=B4 but I cannot figure out the values of the thetas!
 
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  • #2
Try and show a little more work than what you've got.
 
  • #3
Well I know how to solve it for a square loop theta 1 =-theta2=45 degrees
= sqrt2*Mu*I/Pi*R
Now for a rectangle I think that theta1=-theta2 (for sides B1=B3) = -b/(sqrt(a^2+z^2)
and theta1=theta2 (for sides B2=B4) = a/(sqrt(b^2+z^2) and than I add them together but I'm not sure
 
  • #4
Noone can help me with this question?
 
  • #5
This is actually pretty tough. You're going to have to use the Biot-Savart law from scratch. The formula you're trying to use is for a point in the same plane as the wire, and isn't going to work here.

[tex]\mathbf{B}(\mathbf{r})=\frac{\mu_0 I}{4 \pi} \int \frac{d \mathbf{l}\times \hat{\mathbf{r}}}{r^2}[/tex]

You should realize some amount of symmetry. I remember I worked this out once, because I was making rectangular coils for a magneto-optical trap, and it took me a bit. What level of physics is this?
 
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  • #6
Mindscrape said:
This is actually pretty tough. You're going to have to use the Biot-Savart law from scratch. The formula you're trying to use is for a point in the same plane as the wire, and isn't going to work here.

[tex]\mathbf{B}(\mathbf{r})=\frac{\mu_0 I}{4 \pi} \int \frac{d \mathbf{l}\times \mathbf{r}}{r^2}[/tex]

You should realize some amount of symmetry. I remember I worked this out once, because I was making rectangular coils for a magneto-optical trap, and it took me a bit. What level of physics is this?

Slight modification: notice that it should read [tex]\mathbf{B}(\mathbf{r})=\frac{\mu_0 I}{4 \pi} \int \frac{d \mathbf{l}\times \mathbf{r}}{r^3}[/tex].
 
  • #7
Oops, yeah, I forgot the hat, I'll fix mine and let yours be an alternate. :)

Edit: Nvm, the hat on the r vector isn't working... so the later version is the best.
 
  • #8
It's third year...E&M 2..any help? I do know there is symmetry of the horizontal and vertical components, and they all add up to give the total magnetic field
 
  • #9
Actually, I've been thinking about this. You can use the derived result that you mentioned earlier, or start from scratch from Biot-Savart. Either way, it's your homework and not mine. You have to make the effort. If you have, then show use you've made the effort by posting some work.
 

1. What is a magnetic field of a rectangular current loop?

The magnetic field of a rectangular current loop refers to the magnetic field that is produced by a current flowing through a loop of wire that is in the shape of a rectangle. This magnetic field can be visualized as a series of concentric circles around the loop.

2. How is the magnetic field of a rectangular current loop calculated?

The magnetic field of a rectangular current loop can be calculated using the following formula: B = (μ0*I)/2a, where B is the magnetic field, μ0 is the permeability of free space, I is the current flowing through the loop, and a is the length of one side of the rectangle.

3. How does the direction of the current affect the magnetic field of a rectangular current loop?

The direction of the current flowing through the rectangular loop determines the direction of the magnetic field. The magnetic field is perpendicular to the plane of the loop and follows the right-hand rule, where the thumb points in the direction of the current and the curled fingers point in the direction of the magnetic field.

4. How does the size of the loop affect the magnetic field of a rectangular current loop?

The size of the loop, specifically the length of one side of the rectangle, directly affects the strength of the magnetic field. The larger the loop, the stronger the magnetic field will be.

5. What are some real-world applications of the magnetic field of a rectangular current loop?

The magnetic field of a rectangular current loop has various real-world applications, such as in electric motors, generators, and MRI machines. It is also used in particle accelerators, electromagnets, and magnetic levitation systems.

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