# Electrostatics and Magnetostatics

# Electrostatic Energy

## 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 :

So :