Question Details

A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a positron. In the same time t, the work done on the two moving charged particles is

Options

A

same as the same force law is involved in the two experiments.

B

less for the case of a positron, as the positron moves away more rapidly and the force on it weakens.

C

more for the case of a positron, as the positron moves away a larger distance.

D

same as the work done by charged particle on the stationary proton.

Correct Answer :

more for the case of a positron, as the positron moves away a larger distance.

Solution :

Let us analyze the two experiments to understand the motion and work done on the released particles.

In both experiments, a stationary proton is located at the origin. Another positively charged particle is released from rest at a distance d from it.
In Experiment 1, the released particle is a proton (mass mp).
In Experiment 2, the released particle is a positron (mass me).

Both the proton and the positron carry the same positive elementary charge e. Therefore, at the initial distance d, the electrostatic repulsive force acting on both particles is identical and given by Coulomb's Law:
F=14πε0e2d2

However, the mass of a proton is much larger than the mass of a positron:
mpme

Using Newton's second law, a=Fm, the initial acceleration of the positron will be much greater than that of the proton:
apositronaproton

Because of its significantly higher acceleration, the positron will travel a much larger distance spositron than the proton sproton in the same time interval t:
spositron>sproton

The work done by the conservative electrostatic force on a particle moving from an initial distance ri=d to a final distance rf=d+s is equal to the decrease in the potential energy of the system:
W=-ΔU=Ui-Uf=e24πε01d-1d+s

Since spositron>sproton, the final position of the positron is further away, making 1d+spositron smaller than 1d+sproton. Thus, the value in the parenthesis is larger for the positron.

Therefore, the work done on the positron in the same time t is more than that on the proton because the positron moves away a larger distance.

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