Chapter 1

# 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 ? Electrons in an electrostatic field

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 : Previous
Gauss' law
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Capacitors