# Field at the center of a toroidal permanent magnet

1. Jun 29, 2012

### apchar

I'd like to make a strong (~0.5 T) solenoidal field with a permanent magnet for a Faraday rotation experiment. If I take an ordinary cylindrical permanent magnet (with an axial field) and drill a hole down the center of it. What's the field deep inside at the center of the hole? Some of the flux lines are bound to return through the hole. Intuitively it seems like there would be some optimum ratio (outer diameter/inner diameter) of the toroid for maximum field strength at the center.

I remember this is buried somewhere deep in J.D. Jackson's book but cant find it. Like most things in Jackson it's probably compressed into half a sentence.

Thanx

2. Jun 29, 2012

### marcusl

The field should be fairly uniform at the center of a small diameter hole drilled down the length of the magnet. Certainly the homogeneity and strength will vary with geometry. A useful approximate model is to replace the magnet with effective magnetic charges at each pole face. The field at the center is the superposition of the return field that provides continuity of the external field lines and the oppositely directed demagnetizing field that points from one face to the other. For a more precise answer, use COMSOL, EMWorks or similar simulation packages.