Magnetization, coil question

[joker_900]

Homework Statement

A bar of soft iron of cross sectional area A and relative permeability μ is bent into
a ring of radius R. The bar is wound with n turns of a wire carrying a current I. Deduce a value
for the magnetic field in the iron, explaining your assumptions.

(b) A narrow gap of width w is sawn into the ring. Find the magnetic field in the gap.

Homework Equations

The Attempt at a Solution

For part a. I used Ampere's Law with H to get

H = nI/(2*pi*r)
B = μμ0nI/(2*pi*r)

But part b? I thought of trying to do some sort of superposition. Perhaps working out M in the original problem, and then doing the field due to the original problem plus the field due to a small chunk with opposite magnetization. Is this at all on the right lines?

 

[Jhero]

Hello there,

For part b, you are on the right track with the idea of using superposition. Here's how you can approach this problem:

1. Start by finding the magnetic field in the ring without the gap. You can use the same equations you used for part a.

2. Next, consider the gap in the ring. The gap essentially creates a "break" in the magnetic circuit, causing the magnetic field to drop to zero inside the gap. However, this also creates a discontinuity in the magnetic field, which we need to account for.

3. To account for this discontinuity, we can use a boundary condition called the "magnetic flux continuity condition." This condition states that the magnetic flux must be continuous across the boundary of the gap.

4. Using this condition, we can set up an equation that relates the magnetic field inside the ring to the magnetic field inside the gap. This equation will involve the relative permeability of the iron, the width of the gap, and the radius of the ring.

5. Once you have this equation, you can solve for the magnetic field inside the gap. This will give you the final answer for part b.

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