Question

A uniform electric field \[\vec E\]exists between 2 plates, a charged particle enters the space between the plates and perpendicular to\[\vec E\]. The path of the particle between the plates is a:
(A) Straight line
(B) Hyperbola
(C) Parabola
(D) Circle

Answer 1

Hint: When a charged particle enters a space between two plates, where there is a uniform electric field between two plates, the charged particle will start moving towards the positive plate.

Complete solution: The equation of a charged particle entering in a uniform electric field perpendicular to it is given by,
\[y = \dfrac{1}{2}\dfrac{{qE{x^2}}}{{m{v^2}}}\]\[y = \dfrac{1}{2}\dfrac{{qE{x^2}}}{{m{v^2}}}\]
From the above equation, we can see that the path of the particle is a parabola.

The correct option is C.

Note: The charged particles such as an electron undergo deflection due to the force of the electric field. The amount of deflection is proportional to the voltage different between the two plates. The deflection is due to a continuous repulsion and attraction from the two plates on the charge particle. The path taken by the charged particle would be parabolic in nature. An interesting feature is its commonality that bears with the path of the projectile of a mass that is influenced by the gravitational force. This also follows a parabolic path as it descends down. The gravitational force and the mass are analogous to the electric force and the charged particle. Further, both these forces follow the inverse square law principle. The deflection of the charged particle under the electric field finds its applications in the photocathodes, analog based oscilloscopes, electron microscopes etc.