Biot-Savart applied to rectangular coil

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Homework Statement

A rectangular current-carrying coil, with side lengths a and b has N turns. The current, I is stable.
The coil is shorter than its width. Calculate the magnitude of the magnetic field at the centre of the rectangle.

Homework Equations

The law of Biot-Savart (I think).

The Attempt at a Solution

Stupid (I know) - but I am unsure of what to do with the element of Biot-Savart, which concerns the radius.
Perhaps I could divide the rectangle into 4 segments - calculate each segment:
Bsegment = (mu o/4p )(I/R)(cosa +cosb )
and then add them up?

Please, please help me as it is part of a larger assignment involving the effect of a magnetic field on a current-carrying coil.

 

[anathema]

To calculate the magnetic field at the center of the rectangular coil, you can indeed use the law of Biot-Savart. This law states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the point. In your case, the wire is the perimeter of the rectangle and the point is the center of the rectangle.

To use this law, you will need to break down the perimeter of the rectangle into smaller segments, as you mentioned. Each segment will have a length of either a or b, depending on which side it is on. The angle between the segment and the center of the rectangle will also vary, so you will need to take that into account.

Once you have calculated the magnetic field for each segment, you can add them together to get the total magnetic field at the center of the rectangle. Keep in mind that the direction of the magnetic field will depend on the direction of the current in the coil.

I hope this helps you with your assignment. Good luck with your calculations! If you have any further questions, please don't hesitate to ask.