The ultimate speed
Posted in Physics, Charge and fieldIn accelerating particles it was shown that when a charged particle is accelerated the electric potential energy lost is equal to the kinetic energy gained:
This equation shows that particles with the same charge will have the same kinetic energy but travel at different speeds as a result of a difference in mass. This equation was rearranged to give a new equation for the speed of an accelerated particle:
Using this equation to calculate the speed of an electron which has been accelerated through a large potential difference of 300,000V however gives an unusual result:
The electron appears to be travelling faster than light which we know is not possible. A potential difference of 300kV is certainly obtainable, the problem lies with the equation
in particular the expression
which is momentum.
is only an approximation for momentum, albeit a very good approximation at low speeds at higher speeds it becomes less accurate.
Particles, such as electrons, will never exceed the speed of light as these approximations may suggest. However, unlike speed, there are no limits to the energy or momentum a particle can gain.