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Unformatted text preview: Chapter 31 The Electric Potential due to a Continuous Charge Distribution 279 31 The Electric Potential due to a Continuous Charge Distribution We have defined electric potential as electric potential-energy-per-charge. Potential energy was defined as the capacity, of an object to do work, possessed by the object because of its position in space. Potential energy is one way of characterizing the effect, or the potential effect, of a force. In the case of electric potential energy, the force in question is the electrostatic force (a.k.a. the Coulomb force)you know: the repulsive force that two like charges exert on each other, and, the attractive force that two unlike charges exert on each other. The electric potential energy of a charged particle depends on a characteristic of itself, and a characteristic of the point in space at which it finds itself. The characteristic of itself is its charge, and, the characteristic of the point in space is what this chapter is about, the electric potential-energy-per-charge, better known as the electric potential. If we can establish the electric potential-energy-per-charge for each point in space in the vicinity of some source charge, it is easy to determine what the potential energy of a victim charge would be at any such point in space. To do so, we just have to multiply the charge of the victim by the electric potential-energy-per-charge (the electric potential) applicable to the point in space at which the victim is located. In the next chapter, we exploit the fact that if you know the electric potential throughout a region in space, you can use that knowledge to determine the electric field in that region of space....
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