Question

A proton and an electron are released form rest in uniform electric field then the correct statement among the following is [NCERT Pg. 46]
(1) Time required to fall through certain distance is more for an electron
(2) The force experiences by proton will be more
(3) Magnitude of acceleration experienced by proton is more
(4) KE gained by both charges in moving through same distance are equal
(ans. 4)
could you provide an explanation please?​

Answer 1

Given info : A proton and an electron are released form rest in uniform electric field.

To check : the correct statement among the following is ..

1. Time required to fall through certain distance is more for an electron.
2. The force experiences by proton will be more.
3. Magnitude of acceleration experienced by proton is more.
4. KE gained by both charges in moving through same distance are equal.

solution : net force acting on each of them ( proton and electron ) , F = qE

from Newton's 2nd law of motion, F = ma

so acceleration of body, a = qE/m

now time required to travel s distance, t = $\sqrt{\frac{2sm}{qE}$

we know, charge on electron = charge on proton [ just sign are opposite ]

but the mass of proton >> mass of electron

so the  time required to fall through certain distance is more for proton.

magnitude of acceleration experienced by electron is more. [ ∵ a ∝ 1/m ]

force experienced by both particle will be equal in magnitude because charge on each is same.

     kinetic energy = workdone by charge particle to move in electric field.

                             = F.s

here kinetic energy doesn't depend on mass and velocity. it only depends on force and displacement. here force acting on each charge is same and if they displace equal distance then kinetic energy gained by both charges will be equal.

therefore the correct option (4) KE gained by both charges in moving through the same distance are equal.