CRT direction of field in accelerating zone

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acherentia
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My textbook says that since the electrons are accelerated to the right in a CRT the field direction is to the left. This leaves me confused, because according to this model the field lines are pointing out from the electrons instead of pointing into the electrons. I thought that field lines are supposed to point into negative charge? Anyone can tell me where I go wrong?
 
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The front of a CRT is essentially a positively charged plate, while the electron source is essentially a negatively charged point source, so the field direction is from front to back, which is to the left in the case you mentioned.
 
I keep forgetting that a charge cannot feel its own field, so obviously the field is not the electrons' field but a field that the electrons are subject to. Thank you.
 
How does the electric field produce acceleration in the moving electrons?

F=ma=qE?

My textbook gives a value for E CRT of 8.0 X 10^5 N/C. Which if this was a constant number, according to my calculations a=1.41 x 10^17 m/s^2.

But I also know that E=kQ/r^2. Since r is changing as the electrons are moving closer and closer into the field, so r is getting smaller and smaller, shouldn't the value of E be constantly changing.

If the value of E is constantly changing as electrons move closer to it, how did they come up with the number 8.0 X 10^5 N/C for E?