# Magnetic fields and flux

1. Dec 4, 2005

### square_imp

I would like to know what is the relationship between the Magnetic field strength and the flux in a toroidal coil of wire. I have an expression for the magnetic field strength at a distance r but need to know the flux through the coil.

Any help is welcome.

2. Dec 4, 2005

### LeonhardEuler

The flux through a little piece of area is equal to the component of the magnetic field perpendicular to the surface times the area of the surface. When the area is not tiny and the magnetic field varies throughout the area, you must do an integral. This integral would be:
$$\int_A \vec{B}\cdot d\vec{A}$$
$d\vec{A}$ is the normal vector to the surface element with magnitude equal to the area of the surface element. I can't go any farther without knowing the specific form of the expression for the magnetic field strength. I don't know if this is what you were looking for.

3. Dec 4, 2005

### square_imp

Thanks for the help, however in my problem the area is sort of hard to work out. Let me just write the problem out:

A toroidal coil is formed with N evenly spaced turns of wire. Each turn has a rectangular cross section with height h and depth (b - a) where b is the outer radius of the toroid and a is the inner radius.

I have worked out the Magnetic field at radius r to be:

B = (u.N.I) / (2.pi.r) u = permitivity constant

I need to now work out the flux through the wire. The area appears to be simply (b-a) x (h) times the number of turns N. This would give flux as:

u.N.I.(b - a).h.N / (2.pi.r)

however this is not correct for some reason. I am slightly confused by this. Does the flux through the coil mean a different thing than the area the coil encompases? Does it then mean the area of the actual wire itself?

Thanks again.

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