When electrons move regardless of what the voltage is, is the strength of the magnetic field a constant?

When electrons move regardless of the what the voltage is, is the strength of the magnetic field a constant?

My understanding of the ammeter is the magnetic field of the moving electron effectively moves the needle and this tells us the amps. But, this would mean regardless of the voltage all electrons must create the same magnetic field strength?

How do you prove experimentally this is true? Have there been experiments to prove this?