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Work, Energy, and Power


Associated with a charge or charge density, permeating the space surrounding the charge, the electric field at a location represents the capability the charge or charge density has to exert force on another charge were one placed there. The electric field strength tells you how many Newtons of force per Coulomb of charge would exert upon the charge placed in the field.

We employ the concept of the test charge to imagine learning about about the force producing character of the field. Placing the charge in various places, we would learn the strength and direction of the field in those places, how many Newtons of force per Coulomb of charge it represents.

Analogously, we could employ the test charge to learn about the energy storing character of the field between two positions. In this case, we would be learning about the electric potential, or voltage. We could push or pull our test charge around and measure how much work is required to move from point A to point B in the field. Voltage represents hypothetical work, joules of work per coulomb of charge, required to move a test charge from point A to point B within the field under study.

So, in summary, while the electric field represents the ability of a charge (or charge distribution) to exert force on hypothetical charges; the voltage represents the ability of a field to perform work on a hypothetical charge.



DC Current

Let us conceptualize an imaginary construct to help us understand the potential difference across a uniform electric field. This useful conceptual game may also help prepare us for electric circuits much later. Let us imagine a gravitational analog to a DC circuit.

Imagine wooden stairs and a croquet ball. It takes a certain amount of work to carry the ball up the stairs (joules per kilogram). Likewise, in a DC circuit, a battery does work in moving charges from low potential to high potential (joules per coulomb).

Releasing the ball down the stairs leads to the evolution of sound energy from the system as it bounces down. This release of energy is analogous to the heat evolved in a DC circuit from a resister which often derives from the collision of charged particles in the current with the atoms of the resistor medium.

Now imagine that instead of a uniform gravitational field, you have a uniform electric field, and instead of croquet balls, you were moving electric charges from a low potential energy position to a high potential energy position. This is analogous to the work performed by a redox reaction in a galvanic cell, for example. Now, instead of the energy stored in the system through the work being later released as a ball rolling loudly down some stairs, imagine instead the charged particles coming back down the potential gradient within the tungsten filament of an incandescent lightbulb.

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