If an electron enters into a space between the plates of a parallel plate capacitor at an angle α with the plates…

Q: If an electron enters into a space between the plates of a parallel plate capacitor at an angle α with the plates and leaves at an angle β to the plates, find the ratio of its kinetic energy while entering the capacitor to that while leaving.

Sol. Let u be the velocity of electron while entering the field and v be the velocity when it leaves the plates.
Component of velocity parallel to the plates will remain unchanged.

$\large u cos\alpha = v cos\beta $

$\large \frac{u}{v} = \frac{cos\beta}{cos\alpha} $

$\large \frac{\frac{1}{2}m u^2}{\frac{1}{2}m v^2} = (\frac{u}{v})^2 = (\frac{cos\beta}{cos\alpha})^2 $