Magnetic field inside square conductor

[Endurance]

Hello everybody,

I got a small question and was wondering if somebody could help me with that.

Problem:

I have a square conductor with side length m. I am now trying to figure out what the magnetic field B is at any point inside that square.

Here is what I've come up with so far and I think I am pretty close:

The magnetic field at the center is B=(4*u_0*I)/4pi*a)*(cos(pi/4)-cos(3pi/4))

where a=m/2 and u_0= the permeability of free space

But how could I change this now to give me the B field for any point x,y inside that loop?

Thanks,
Endurance

 

[Jhero]

Hello Endurance,

Thank you for your question. The equation you have come up with for the magnetic field at the center of the square conductor is correct. However, to find the magnetic field at any point (x,y) inside the loop, you will need to use the Biot-Savart Law, which is given by:

B = (u_0 * I)/(4 * pi) * ∫(dL x r)/r^3

where u_0 is the permeability of free space, I is the current, dL is the differential length element along the current, r is the distance from the current to the point of interest, and the integral is taken over the entire current-carrying loop.

To use this equation for your square conductor, you will need to divide the loop into smaller segments and integrate over each segment to find the total magnetic field at the point (x,y). This integral can be solved numerically using a computer program or by hand using calculus techniques.

I hope this helps. Let me know if you have any further questions.