Stern Gerlach Gradient Field Strength

[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

 

[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.

 

[denian]

Hello Robert,

Thank you for sharing your interest in recreating the Stern-Gerlach experiment. The gradient magnetic field strength can be calculated using the formula:

B = μ0 * (m1-m2) / (2 * d)

where B is the magnetic field strength, μ0 is the permeability of free space (4π*10^-7 T*m/A), m1 is the magnetic moment of the sharp-edge magnet, m2 is the magnetic moment of the flat magnet, and d is the distance between the two magnets.

To calculate the magnetic moment of the magnets, you can use the formula:

m = m0 * A * n,

where m0 is the magnetic moment per unit volume, A is the cross-sectional area of the magnet, and n is the number of magnetic domains in the magnet.

Once you have calculated the magnetic field strength using the first formula, you can use this value to determine the deflection of the electron in terms of the gradient field.

I hope this helps and good luck with your experiment! If you have any further questions, please don't hesitate to ask.