Direction of Magnetic Flux Density in Velocity Selector

Question

In a velocity selector (a.k.a. Wien filter), we have a positively charged plate and a negatively charged plate, with the (conventional) current travelling from the positive to the negative end. According to the Right-Hand Grip Rule, this would then create a magnetic field (flux density) $\boldsymbol{B}$ in a direction counterclockwise around the current, and hence I thought that the right side would have the field lines going into the page while the left side would have the field lines going out of the page, but in reality the magentic field points uniformly out of the page. Why is this wrong?

Answer 1

Your thinking is incorrect because the source of the magnetic flux density in a Wien filter is not a current flowing between the two plates. In fact, there is no meaningful current between the plates at all. The source of the electric field is essentially a simple plate capacitor, which in steady state requires no current to be maintained. The source of the magnetic field is simply external to your diagram, and could be something like a solenoid (for example).

The magnetic and electric fields in this device are created by two different sources, and do not explicitly have anything to do with one another. The design of the device keeps them orthogonal, but the freedom to vary their magnitudes is what allows particles of specific velocities to be selected for.

Answer 2

There isn't any current between the two plates (the velocity of the charge is not in the direction of the electric field). There is a big difference between current and electric field.