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Let consider that we are using parallel plates to create electric field. And let assume that there are small holes in both the plates (holes on both the plates are aligned). Now if we bring a electron (moving at certain velocity) and make it pass through the holes in plate, will there be any force on plates.

Assuming electron enters from positive plate and passes through it without sticking to the positive plate.

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  • $\begingroup$ Is this a homework question? What have you tried to do and where did you get stuck? $\endgroup$
    – Quantum Mechanic
    Commented Jan 21, 2022 at 17:10
  • $\begingroup$ You might find it easier to consider first the force on the electron due to the plates. $\endgroup$
    – Philip Wood
    Commented Jan 21, 2022 at 17:31

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I think that depends on what the plates are made of whether they are conductors or dielectrics.

If the plates have equal but opposite charge densities, then their field only exists between them since they each produce a constant field (to good approximation). Those field add between the plates, but cancel above and below the plates.

Now introduce the electron. I'd expect this to induce a charge on the plates, concentrating positive charge on the part of the plate closest to the electron. I think you can actually calculate that using The Method of Images. The method changes between conductors and dielectrics.

I'd expect shifts also to occur to the negative plate.

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  • $\begingroup$ What type of shift ? (In last paragraph) $\endgroup$
    – Kaushik Kumbhat
    Commented Jan 22, 2022 at 2:21
  • $\begingroup$ The electron draws charge towards it in the positive plate. That assymetric distribution of positive charge draws negative charge to the nearest point on the negative plate to the positive plates accumulated positive charge. $\endgroup$
    – R. Romero
    Commented Jan 22, 2022 at 5:24
  • $\begingroup$ What If I keep negative plate before positive plate (with less charge than positive plate). Will there be any force on negative plate. If yes then how much? $\endgroup$
    – Kaushik Kumbhat
    Commented Jan 22, 2022 at 8:37
  • $\begingroup$ Similar principle applies, Constant field between the plates, no field out. This time the electron pushes charges away from the nearest point on the negative plate, effectively increasing the local charge distribution. That in turn should have a repelling force on the positive place. In other words, the reverse of the previous case. As to exact forces, I think the method of images would help there. With a single, neutral conducting plate, you can pretend there's an equal but opposite charge within the plate the same distance within as the electron is above. Gets more complicated if charged. $\endgroup$
    – R. Romero
    Commented Jan 22, 2022 at 20:46

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