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?
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.
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.
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.
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.
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.