## Energy in a Uniform Electric Field

When an electric charge is placed in an electric field, it experiences a force. This means that if it moves from one point to another, in general, electric potential energy will be lost or gained: work will be done. If the charge moves in the direction of the force on it, it will lose electric potential energy and if it moves in opposition to the force on it, electric potential energy will be gained.

If the field is uniform the force will be constant, since The change in electrical potential energy is given by where is the distance moved in the direction of the field as shown below. Alternatively we can write where as before is the distance moved and now is the change in potential as the carge q moves from the start point to the end point. Then the change in electrical potential energy is This change in potential energy will result in a change in speed of the particle. A fall in electrical potential energy will result in an increase in kinetic energy because total energy is conserved. If the particle starts from rest then, it will move in the direction of the force on it.

Fall in electrical potential energy = increase in kinetic energy  