# A question about the Thomson experiment

Recently, I was studying about Thomson's experiment with cathode rays. My textbook shows it like this.

It says:

When only electric field is applied, the electrons deviate from their path and hit the cathode ray tube at point A. Similarly when only magnetic field is applied, electron strikes the cathode ray tube at point C.

But if we apply Fleming's Right Hand Rule, then we get the direction of force in the upward direction, so the rays should deviate towards A but they deviate towards C. I think it is because Fleming's Left Hand Rule is defined for conventional current(flow of positive charges) and what we are dealing with are negative charges. Is that correct?

Fleming's right-hand rule applies when a conductor is moving in a magnetic field and the current is induced. However, in this case, we have a charged particle moving through a non-varying magnetic field, so it's Lorentz magnetic force law that applies best here. The simple form, in which there is only a magnetic field component (and no externally applied electrostatic field) is this: $${\bf F} = q({\bf v} \times {\bf B})$$ in which ${\bf F}$ is the force vector, $q$ is the charge of the moving particle, ${\bf v}$ is the velocity of the particle and ${\bf B}$ is the magnetic field vector. If we apply the right hand rule to this (the direction of any cross product of vectors can be visualized by using a right hand rule), we see that ${\bf v}$ is to the right when viewing your diagram and ${\bf B}$ is coming out of the page (in the direction of N to S of the magnet) and so the resulting ${\bf F}$ is pointing down.

However, because the charge $q$ is negative, the sign of the resulting vector ${\bf F}$ is reversed, so the force is upward. The diagram is incorrect and should show reversed N and S poles of the magnet (or equivalently, reversed electrode polarity).

Note, too, that Fleming's left-hand rule (current and magnetic field are given, and force is the result) will also work for direction here because, as you correctly point out, Fleming's left-hand rule is given in terms of "conventional current" (from + to -) rather than electron flow, and electron flow is clearly left-to-right in the diagram. For the force to be pointing down, again the poles must be reversed.

Here is a similar diagram figure 2.4 from publisher Prentice-Hall which correctly shows the opposite polarity for the electrodes.

• But I thought Fleming's Left Hand Rule gives the direction of force acting on positive charges. So, shouldn't the force acting on negative charges be just opposite to that acting on positive charges? – Yashbhatt Jul 15 '14 at 17:43
• @Yashbhatt: Yes, your understanding is correct, and the textbook is in error. The diagram should have N and S reversed. I've updated my answer to account for this. – Edward Jul 15 '14 at 22:36
• What I understand is that the diagram is correct because from Fleming's Left Hand Rule, we get the direction of force acting on positive charges but as cathode rays are negatively charged they should move downward. – Yashbhatt Jul 16 '14 at 15:09
• @Yashbhatt: No, Fleming's left-hand rule refers to the force on a conductor due to the interaction between a current and a magnetic field. The charge of the actual particles that make up the current don't matter (except in determining the direction of the current), since it's the movement of the charges that are required for any force to be developed; an unenergized electric motor has no torque. – Edward Jul 16 '14 at 23:49
• The direction of motion of charges in this figure has to be taken towards the right, right? – Yashbhatt Jul 17 '14 at 13:36