# Electrons in motion

## Question:

Please can you tell me something about the equation of motion of electrons.

In electric fields:
Force = ma and since
Force in an electric field = Eq the equation becomes
Ee = ma for an electron of charge e. The exact equation of motion will depend on the shape of the electric field.
The kinetic energy of the electron will increase as its linear velocity increases.
In an electric field the electron will accelerate towards the positive point in the field. In a uniform field (like that between two charged plates) the acceleration will be constant.
However a radial filed (like that produced by a single positive or negative charge) the acceleration will vary depending on the distance of the electron from the central charge.

In magnetic fields:
Here the electron will move in a circle according to the equation F = Bev where v is the electron velocity at any point and B is the field strength.
The force on the electron will always be at right angles to the electron's motion (force on a current in a magnetic field and Fleming's left hand rule).
In a uniform magnetic field the electron will move in a circle – this means that there will be a centripetal force and so a centripetal acceleration but the speed (and the kinetic energy) of the electron will remain constant.

In gravitational field the electron will behave like any other body with mass. However the electron speeds are usually so great and its mass is so small that electrons effectively move in straight lines in gravitational fields of strength similar to that of our planet.

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