Electrostatics and Magnetostatics
Fondamental : Potential energy of a punctual charge q located at the point M under a potential V(M)
A particle of charge is placed in an area of space where an electrostatic field reigns. It derives from the potential as such :
The charge is subject to the force :
Hence the potential energy of the charge is :
Attention : Potential energy of a punctual charge q located at the point M under a potential V(M)
Exemple : Linear electron accelerator
Electrons are accelerated in a straight line (in empty space) from a metal electrode which has a potential equal to zero to a metal electrode which has a potential .
The first electrode is slightly heated, which allows the electrons to come out of it by thermoelectric effect.
Their initial velocity is approximately equal to zero ( ).
How can the velocity of the electrons when they arrive to the second electrode be determined ?
The mechanical energy conservation of an electron can be used.
When the electron has the potential of the second electrode, this energy can be expressed by :
Initially, the velocity and the potential are equal to zero.
Finally, the mechanical energy is equal to zero.
Hence, the velocity of an electron when it reaches the second electrode verifies :