Steve4Physics said:
Hi
@phantomvommand.
What do you mean by 'in the hole of the toroid'? Do you mean at the geometrical centre-point (on the central axis, in free space)?
The Homework Statement says: "B(D - r)/mu + Br = mu0 N I"
But you then state: "B(D - d)/mu + Bd = mu0 N I"
So 'r' has changed into 'd'. This suggests you might have accidentally changed a radial value to a diameter value.
Does 'average diameter 'D' mean the overall diameter of the toroid or is it the diameter of the coil of wire?
Your value of 'mu0' has missing units,
We use ##\mu_r## for relative permeability.
##\mu## means absolute perpemeability: ##\mu = \mu_r \mu_0##
You need to indicate what have youu tried so far (e.g. links and insights from searching for 'magnetic field at centre of toroid').
You need a diagram. And it's best to use Latex for equations. You'll get a better response that way.
Was my reply to your earlier post
https://www.physicsforums.com/threa...plasma-due-to-a-nearby-electron-beam.1002420/ helpful?
Yes, I realized my mistake. the 'd' is correct, and it refers to the diameter of the hole in the toroid. I am assuming 'D' refers to the overall diameter of the toroid, taken at a radius (r1 + r2)/2 away from the centre of the toroid, where r1 and r2 are the inner and outer radii of the toroid. (This is probably what is meant by "average diamater.")
Yes, i did not type in the units for ##\mu_0##. Apologies for this.
The book where I took this question from refers to the relative permeability as ##\mu##. Thank you for highlighting this distinction. Side note: This book has multiple printings errors. If your solution suggests that mu is in fact the absolute permeability, instead of the relative permeability, please do share it with me still, as this could be yet another typo.
I have found the following:
https://physics.stackexchange.com/questions/381232/magnetic-induction-at-the-centre-of-a-toroid
This suggests that there is a downward magnetic field at the centre of the coil, equivalent to ##\mu_0*I*\pi/d##, where d is the diameter of the "hole".
Side note: It is quite uncommon to work with diameters instead of radii, and one should take note of this.
As usual, the magnetic field in the toroid can be found with ampere's law. I am puzzled about the fact the 2 terms add together to give the term on the Right hand side, which resembles Ampere's Law. If you apply Ampere's Law to a loop inside the toroid, one can find an expression for the magnetic field inside the toroid (very standard), and you can express the field inside the toroid in terms of the field in the centre of the toroid. I suppose that because relative permeability is involved, when applying Ampere's Law for a loop inside the toroid, ##\mu_0## should be replaced with ##\mu##.
Apologies for not presenting the equations nicely with Latex. I am still in high school, and have not yet had the time to learn Latex.
Yes, you reply to my previous post was very helpful, thank you very much!
This question was taken from Experimental problem 1, Part 4, of the 2004 Asian Physics Olympiad, where the equation in question was mentioned; I am wondering about its proof.