# Magnetic Field of rectangular current loop

• cconfused

## 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!

Try and show a little more work than what you've got.

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

Noone can help me with this question?

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.

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

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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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.

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

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 $$\mathbf{B}(\mathbf{r})=\frac{\mu_0 I}{4 \pi} \int \frac{d \mathbf{l}\times \mathbf{r}}{r^3}$$.

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.

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

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.