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Work Done in Electric Fields

Physics (Year 12) - Electro-magnetism

Dev Lohar

Electric Potential Energy

Similar to how there is gravitational potential energy, there exists a similar entity in electromagnetism; electric potential energy. Electrical potential energy is a form of energy that is stored in electric fields. Whenever a charged object is moved or moves (by itself) from one point in an electric field to another point, work is done on that charged object by the electric field or work is done on the electric field. This work done can be calculated through the following relationship:

By combining the above equation with the voltage equation we learnt in the previous section, V=Ed, we end up with an equation which tells us the work done on a positive charge to move it across a voltage (i.e. potential difference).

After calculating the work done on a charged object, or in other words calculating how much energy it has gained, it is possible to find its speed after it has gained that certain amount of energy. This can be easily done by using the kinetic energy formula;

Work Done on or by an Electric Field

As we learnt above, the work done can be either on a charged object by an electric field or on an electric field by forcing the object to move. How do we determine which one it is?

If an electrically charged object inside an electric field is moving in a direction it would naturally move (due to the laws of nature), then work is done on the object by the electric field. For example, a proton moving from a positively charged plate to a parallel negatively charged plate.

If the object is forced to move against the direction it would naturally go, then work is done on the electric field by the charged object. For example, a proton moving (or being moved) from a negatively charged plate to a parallel positively charged plate.

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