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HyperPhysics - Isolated Sphere Capacitor?
Capacitance is a broader concept than simply for describing parallel plate capacitors. If you are thinking about the relationship between the geometry of a charge distribution and its potential (a kind of thinking which is very important in chemistry) you are applying this broader sense of capacitance. The isolated sphere is a good model system for this type of thinking.



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In many college physics courses, the discussion of capacitance often stays at the level of describing circuit elements. The idea of capacitance is restricted to describing what happens with certain types of electrical devices that can store energy in the electric field between a pair of closely spaced plates.

However, in this review course, I want to encourage you to develop a more general sense of capacitance. The unit of capacitance is the farad, which is a a coulomb per volt. What does it mean, for there to be a relationship between the amoung of charge and the potential function.

What capacitance describes is the relationship between the geometry of a charge density and its voltage. Capacitance describes a geometry, a situation for charge. When you ask what the arrangement of charge does to its voltage, you are discussing the idea of capacitance. Think about it. A compressed small sphere of like charge has a higher voltage than a larger sphere with the same amount of like charge spread on it. It would take energy to push the charge on that larger sphere into the smaller volume. What we just said is that the larger sphere has a higher capacitance because it can hold more charge before reaching a given voltage.

This general, conceptual sense of capacitance is a useful conceptual framework to bring to chemistry. That is why we are going through this discussion, really, to give you something to chew on for chemistry, even though the nomenclature is not generally used in chemistry. In chemistry, you are often asked to interpret how changes in a charge distribution affect the energy. When like charge is permitted to spread out over greater volume, the voltage of the charge distribution decreases. It has lower energy. Geometries which are spread out generally have greater capacitance than compact geometries. As an example using the capacitance of spheres, can you explain why hydrochloric acid is a stronger acid than hydrofluoric acid?








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