A proton is kept at rest. A positively charged particle is . . .

Question : 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 a proton and in another a positron. In the same time t, the work done on the two moving charged particles is 

a) same as the same force law is involved.
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. 

Doubt by Muskan

Ans : c) is the correct option.

Detailed Solution : 

Here you need to know that positron is an antiparticle of electron. Wait a minute, what does that mean? It simply means that the charge on positron will be equal and opposite to that of electron but its mass will be same as that of electron. 

So both the proton and positron have same charge so the magnitude of electrostatic force of repulsion will be the same. But the mass of positron will be much less than the mass of proton. Hence, the displacement covered by the positron will be much greater than that by proton in the same Electric field and the same time t. 

F=ma
F=constant 
ma=constant
So
a∝1/m — (1)
Also
s=ut+½at2
but u=0
so
s=½at2
s∝a [t = same for both]
s∝a∝1/m [Using (1)]
or
s∝1/m — (2)
Also,
Workdone = Force×Displacement
F = constant for both
W∝s
W∝1/m [Using (2)]
mpositron<mproton
Wpositron>Wproton

So, work done by the positron will be much more than that of proton.

Hence, c) would be the correct option.