0
$\begingroup$

This image below show the movement of an electron in a magnetic field, it's taken from the video [Histoire des sciences] La découverte de l'électron explaining the experience of J.J. Thompson when he discovered the electron.

                    Cathode ray tube

I don't understand why electrons are going the way indicated the red dotted line. Below is how I understand this image with the right-hand rule:

Cathode ray tube (edited)

Because the force $\vec{F}$ is oriented toward the top, a positively charged ion (or cation) should go toward the top as shown on the picture. But here, it's an electron, a negatively charged particle, so it should be going toward the bottom. So why is it going toward the top? What's wrong in my understanding?

Also, is it correct to mark a plus (+) and a minus (-) on the magnet?

$\endgroup$

1 Answer 1

1
$\begingroup$

The force on a particle with charge $q$ and velocity $\vec{v}$ due to a magnetic field $\vec{B}$ is given by $\vec{F} = q(\vec{v} \times \vec{B})$. For an electron, $q$ is of course negative. For the geometry in the figures you posted, $\vec{v} \times \vec{B}$ points downward, and hence the force is upward.

In terms of the vectors in the second figure, I suppose $\vec{I}$ indicates the direction of current flow, which is in the opposite direction of electron flow. The right hand rule says that the force is in the direction of $\vec{I}\times\vec{B}$, which again is upward, as you can deduce by aligning your thumb with $\vec{B}$ and your middle finger with $\vec{I}$, whereby your index finger will point upward. For a positively charged particle, $\vec{I}$, and hence $\vec{F}$, would have the opposite orientation.

Marking a whole magnet plus or minus doesn't make much sense. Magnets have two poles: north and south. Outside the magnet, $\vec{B}$ tends to point from north to south. In this case, the magnet you labeled with a plus likely has its north pole facing the tube, while the other magnet has its south pole facing the tube. The two cylinders in the figure could also be (and I suppose usually are in practice) two different poles of the same magnet.

$\endgroup$
2
  • $\begingroup$ Sorry, I still don't see what's wrong in my understanding... $\endgroup$
    – DevonDahon
    Jul 16, 2019 at 15:05
  • $\begingroup$ With $\vec{I}$ oriented as shown in your second figure, you will find by applying the right hand rule that $\vec{F}$ is upward. But this direction of $\vec{I}$ assumes that the particles are negatively charged: otherwise $\vec{I}$ would point in the opposite direction and $\vec{F}$ would be downward. $\endgroup$
    – Puk
    Jul 16, 2019 at 19:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.