Problem 34.

A particle of charge Q and mass m is accelerated from rest through a potential difference V, attaining a kinetic energy K. What is the kinetic energy of a particle of charge 2Q and mass m/2 that is accelerated from rest through the same potential difference?

Solution

We need to use the energy conservation law: the work done by electric force is equal to increase of the kinetic energy of the particle. The work done by electric force is equal to the product of the charge of the particle and the potential difference: . Then the kinetic energy is

.......................................................................(1)

(the initial kinetic energy is zero).

For the particle with charge 2Q and mass m/2 we have the same expression but know with the charge of the particle 2Q:

Taking into account expression (1) we obtain:

Interesting, the result does not depend on the mass of the particle.