So we know that, for example, a stretched elastic band has elastic potential energy (stored energy). Well, charged particles can in fact also store energy. If you try to push like charges together the charges repel each other so you have to do work to decrease the separation between them. All the work done is stored as electric potential energy. This is recovered when you let go.
So we already know that F = Qq/4πε0r2.Underneath the force-distance graph is the work done. The total work done to bring the particles from infinity to a separation r is the total area under the graph. The total work done is the same as the electric potential energy 'E':
E = Qq/4πε0r
Electric potential
The electric potential 'V' at a point is defined as the work one per unit charge in bringing a positive charge from infinity to that point. If the test charge is q, the equation for V can be determined by dividing the electric potential energy E by q:
V = E / q= Qq/4πε0rq = Q/4πε0r
NOTE: The units for electric potential 'V' is J C-1.
Electric potential difference (electric p.d.)
The electric potential difference is the work done per unit charge between two points around the particle of charge Q. It is essentially the difference in the potentials at two points.
Capacitance
This is the last little bit of electric fields....
A capacitor is a device that stores charge. As isolated charged sphere of radius R also stores charge. It too is a capacitor. The capacitance 'C' of a charged sphere is the ratio of the charge it stores , Q, to the potential electric potential 'V' at its surface:
C = Q / V = 4πε0RV / V = 4πε0R
This is the capacitance of an isolated sphere (one that is very far away from other objects).
NOTE: we need to be able to derive this equation (from Q = VC and V = Q/4πε0r)
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