Magnetic field?

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This was something mentioned in an electronics class today (it's an oscilloscope). I didn't copy it down when I should've, but I was listening rather than scribbling. I hope that I reproduced it properly.

The professor was trying to explain how the cathode ray tube would emit electrons when heated up (which I have represented as a beam for ease of drawing). These would travel through the vertical deflection plates and experience a sideways force due to the electric field. Then they would go through the horizontal plates and be deflected again before being displayed on the screen.

My question is, why is there no induced magnetic field? Is this because the prof was assuming the field between the plates is uniform?

If there was hypothetically a changing electric flux, then there would be an induced magnetic field. My question is, if this were the case, would the electrons experience another force? Would this force deflect the electrons?
 

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Consider the Maxwell–Ampère law [itex] \vec\nabla \times \vec H=\vec J + \frac{\partial \vec D}{\partial t} [/itex] which for your case becomes [itex] \vec\nabla \times \vec H= \frac{\partial \vec D}{\partial t} [/itex]. So the electric field generates a magnetic field, only if its changing with time. So the professor was assuming that the electric field is independent of time.

Yes, if the electric field was changing in time, it would produce a magnetic field and the magnetic field would deflect the electrons further.
 
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