# Stern Gerlach Gradient Field Strength

1. Jun 10, 2008

### rwhitman

I am trying to recreate the Stern-Gerlach experiment and am having trouble trying to calculate the gradient magnetic field. I am using two magnets with one having a sharp edge and the other flat. I have calculated what the deflection will be of the electron will be in terms of the gradient field, but I do not know how to calculate what the gradient is knowing the dimensions of the magnets.

~Robert

2. Jun 10, 2008

### Hans de Vries

Make sure you use the gradient of the inproduct of the magnetic moment and the
magnetic field rather than the gradient of the magnetic field itself.

$$\vec{F}_{magn}\ =\ \textsf{grad}\left( \vec{\mu}_e\cdot \textsf{B} \right)$$

What you could do is assuming that every little volume of magnetic material is a
point dipole field like this:

$$\textsf{B}~ = ~ \ \frac{\mu_o\mu_e}{4\pi r^3}\ \ \left(\ 3\ \frac{xz}{r^2}, \quad 3\ \frac{yz}{r^2}, \quad 3\ \frac{zz}{r^2}-1\ \right)$$

Assuming that they all point in the same direction you can derive the total
magnetic field by integration (analytic or numerical)

Regards, Hans.

Last edited: Jun 10, 2008