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
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 from it.
In Experiment 1, the released particle is a proton (mass ).
In Experiment 2, the released particle is a positron (mass ).
Both the proton and the positron carry the same positive elementary charge . Therefore, at the initial distance , the electrostatic repulsive force acting on both particles is identical and given by Coulomb's Law:
However, the mass of a proton is much larger than the mass of a positron:
Using Newton's second law, , the initial acceleration of the positron will be much greater than that of the proton:
Because of its significantly higher acceleration, the positron will travel a much larger distance than the proton in the same time interval :
The work done by the conservative electrostatic force on a particle moving from an initial distance to a final distance is equal to the decrease in the potential energy of the system:
Since , the final position of the positron is further away, making smaller than . Thus, the value in the parenthesis is larger for the positron.
Therefore, the work done on the positron in the same time is more than that on the proton because the positron moves away a larger distance.
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