In: Physics
An electron and a proton, starting from rest, are accelerated through an electric potential difference of the same magnitude. In the process, the electron acquires a speed ve, while the proton acquires a speed vp. Find the ratio ve/vp.
Solution:
Since the particles are accelerated from rest, the total energy available in the form of potential energy by the particle is converted to kinetic energy, E = KE
The kinetic energy, K = 1/2 m v2where
m is the mass of the accelerated particle
v is the velocity with which the particle is accelerated
The electrostatic potential energy of the particle is, E = qV where
q is the charge of the particle
V is the potential of the region
For an electron,
Equating these two,
Similarly for a proton,
Taking the ratio of ve and vp
( cancelling potential from numerator and denominator since the potential experienced is the same for both the particles)
since the magnitude of charges are the same we can cancel out that also
Therefore,