Infinitely Long Parallel Rectangular Parallel Strips (H field)

[jegues]

Homework Statement

See figure attached.

Homework Equations

The Attempt at a Solution

I have some concerns about his solution for part a).

I agree with how he's evaluated Ampere's law to find the field due to one of the strips at any point between the plates, but if you want to know the net field inbetween the strips, I think you must consider what the opposing plate is doing as well.

He seems to have neglected this, am I correct?

For example, let's say we want to find the field a distance z from the bottom plate, or in other words a distance (a-z) from the top plate. (Assuming the Y-axis starts at the top edge of the bottom plate)

The net field should have two contributing fields, one from each plate respectively.

Does it just so happen that due to the symmetry of the problem that the summation of these two contributing fields always works out to be the answer he's given? (Anywhere inbetween the two plates of course)

How can you prove that this is indeed the case?

 

[jegues]

Still looking for some help!

 

[omoplata]

I am unsure about the reasoning that I'm about to present, so check with someone else before accepting it.

It seems that he has indeed considered the opposing plate, because he's using the approximation that the field outside the two strips to be zero. If the two currents that are flowing in the strips were not equal in magnitude and opposite in direction, then there would be a net current flowing in one direction, and thus, according to the Ampere's circuital law, there would be a resultant non-zero magnetic field on the outside.

 

[jegues]

I am unsure about the reasoning that I'm about to present, so check with someone else before accepting it.

It seems that he has indeed considered the opposing plate, because he's using the approximation that the field outside the two strips to be zero. If the two currents that are flowing in the strips were not equal in magnitude and opposite in direction, then there would be a net current flowing in one direction, and thus, according to the Ampere's circuital law, there would be a resultant non-zero magnetic field on the outside.

He states in the question, "Assuming that the magnetic field is contained entirely between the strips" so there is no field outside.

 

[omoplata]

He states in the question, "Assuming that the magnetic field is contained entirely between the strips" so there is no field outside.

I think that assumption can only be made if the currents in the strips are equal in magnitude and opposite in direction. Because if you apply Ampere's circuital law to a loop around both strips, if there is a net current in one direction, the line integral of the magnetic field is going to be non-zero.

So, if the currents are not equal in magnitude and opposite in direction, a zero outside magnetic field is a physical impossibility, and implies that the Ampere's circuital law is wrong.

Anyway, I would also welcome someone else's opinion on this.