Alpha and beta in a magnetic field
Fleming's left-hand rule links current, magnetic field and force
Moving charges in a magnetic field experience a force.
Fleming’s left hand rule tells you the direction of the force if you know the directions of the electric current and the magnetic field.
Similarly if you know the direction of the force and the direction of the magnetic field then you can infer the direction of the electric current. Since alpha and beta particles are charged they make up a very small electric current.
The trick is to see whether the direction of the current you come up with from using Fleming's left-hand rule is the same as the direction you know the particles are moving in (because you know they come from the source).
Conventional current is the movement of positive charges
We have to use ‘conventional’ current with Fleming's left-hand rule. Conventional current is the direction that positive charges would flow in.
If it’s really negative charges that are flowing then we have to replace them with imaginary positives flowing the other way.
So if Fleming's left-hand rule tells us positives are flowing in one direction and we know that in reality our charged things are flowing in the other direction then we know that our charged things must be negative.
Alpha and beta move in circular paths in a magnetic field
In magnetic fields charged particles tend to move in circles. This is because the force is always at right angles to the direction the particle is moving at each instant as it curves.
We know the direction of the force because we can see the direction the particles curve. The force points towards the centre of the circle.
Let’s look at the alpha particles first. We point the first finger in the direction of the field and the thumb in the direction of the force.
We know the alphas must be moving from left to right (away from the source) and our second finger shows that this is the direction of the conventional current.
The alphas are moving in the same direction as the conventional current so they must be positively charged.
Beta particles move in the opposite direction to conventional current
Again with beta particles the thumb points towards the centre of the circle the beta particles follow and the first finger points in the direction of the magnetic field.
The second finger shows which direction conventional current would have to flow to cause this kind of motion.
But the beta particles must be moving in the opposite direction to the conventional current (the direction positive charges would move) because we know that they come from the source.
This means beta particles must be negatively charged.