Finding the Magnetic Field of two slabs.

[georgedaisuki]

Homework Statement

There are two slabs on one another. The top slab has current coming out of the page and the bottom slab has current going into the page. y=0 is located between the two slabs. the current density of the top slab is J and the current density of the bottom slab is -J.

Homework Equations

Is the magnetic field due to the top slab the same as the magnetic field due to the bottom slab?
At y=0, what is the magnetic field?

The Attempt at a Solution

Finding the magnetic field of one slab with current going one way is easy enough but I am confused the properties of the magnetic field with two slabs on one another. I thought that at y=0, (between the slabs) since there's no current at y=0, the magnetic field would be zero. But I realized that at y=0, this location will experience magnetic field from both the top and the bottom. So what is the amperian loop for this? Will the loop contain both 2 slabs or will the loop be a box inside the two slabs..?

 

[Nate810]

Would the magnetic field be twice as strong as the magnetic field due to one slab? Is the magnetic field at y=0 the same as the magnetic field due to one slab? I am so confused. I need help.

 

[nlightner]

I would like to clarify that the magnetic field at a point is the result of the vector sum of the fields due to all sources present at that point. In this case, the magnetic field at y=0 will indeed be the sum of the fields due to both slabs. The Amperian loop for this situation will enclose both slabs, as the magnetic field due to each slab will contribute to the total field at y=0.

To find the magnetic field at y=0, you can use the superposition principle and consider the fields due to each slab separately. The field due to the top slab can be calculated using the Biot-Savart law, and the field due to the bottom slab can be calculated by flipping the direction of the current and using the same equation. The resulting fields can then be added together to find the total magnetic field at y=0.

It is also important to note that the magnetic field inside a conductor is zero, so the magnetic field at y=0 will only be due to the current flowing in the slabs and not the material of the slabs themselves. I hope this helps in finding the magnetic field at y=0 between the two slabs.