Which pair of values will cause the greatest deflection of an electron beam in a cathode ray tube?

Question

41.) Which pair of values will cause the greatest deflection of an electron beam in a cathod ray tube?

A.) 400 V Accelerating; 40 V Deflection (Plate)

B.) 400 V Accelerating; 20 V Deflection (Plate)

C.) 800 V Accelerating; 20 V Deflection (Plate)

D.) 800 V Accelerating; 40 V Deflection (Plate)

Answer: A

can someone please explain? thanks!!

Answer 1

An E&M question, what fun. Here goes:

The electron is being accelerated by the electric field that exists between the two plates in the CRT. I'm just considering one electron because this happens one electron at a time. You could slow down the CRT to see it happening one at a time, if you wanted.

Anyway, we know the equation that describes the magnitude of the potential difference (voltage) between the two plates (this is given by Gauss's law):

V=E*d

where

V=voltage

E=magnitude of electric field

d=distance between the plates

We have V between the plates given, which is nice. We assume each of the hypothetical pairs is separated by the same distance, so V is directly proportional to E.

Deflection is caused by the force resulting from the E field, exerted on the electron. instantaneous Force= voltage * charge

total Force is equal to mass*acceleration (in the direction of deflection, perpendicular to the initial acceleration)

We know the mass=9.11 * 10^-31 kg

and the charge of an electron=1.602*10^-19 coloumbs

These are constants. Finally, the change in momentum= time integral of force. That is, if you integrate the force exterted by the field over the length of time between the plates, you'll get the "kick" provided to the electron that causes it to deflect.

If the electron is initially going very fast, the E-field won't have much time to deflect it. So there is a trade off going on.

So we want something that is moving slow enough to get enough "kick" while its between the plates, and we want plates that are charged enough to "kick" it a lot.

So without actually doing any math, we can see that answer A, which combines a slow initial speed (results from initial horizontal acceleration at electron gun, then is constant) with a high plate voltage, will provide the most "kick" and therefore the most displacement.

Hope this helps!! Sorry for all the math, kind of went a bit overboard.

Answer 2

A volt is a unit of electrical force or pressure.

400V doesn't "push" as hard as 800V.  Since 400V pushes less, electrons won't go as fast as the would with 800V of push.  Since the electrons being pushed by 400V are slower, they take longer to travel the length of the tube.  The longer they travel, the more time a deflecting force can act on them.

While the electron is traveling to the screen, it is being pushed from the side by either 20V or 40V.

Once again, the 40V "pushes" harder so it will deflect the electron more than 20V.

The worst case scenario is a slow electron being deflected by the greatest force.  400 V accelerate; 40 V deflection.

Answer 3

A   is a slow speed of the electrons and the 40V is a higher sideways push or pulling force

I hope you wanted the simple explanation