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

 

[Endurance]

Is this too advanced for this section? Do I maybe have to post this in the Physics with calculus section?

 

[ogb p]

Hello Endurance,

Your approach to finding the magnetic field at the center of the square conductor is correct. To find the magnetic field at any point inside the conductor, you can use the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current and inversely proportional to the distance from the current-carrying element.

In this case, the current-carrying element is the square conductor, and the distance from the point to the conductor can be found using the Pythagorean theorem. You can then use the Biot-Savart law to calculate the magnetic field at any point inside the conductor.

However, keep in mind that the magnetic field inside the conductor will not be uniform, as it depends on the distance from the current-carrying element. It will be highest at the center and decrease as you move towards the edges of the square.

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

Best,