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Electric potential The electric potential at a point in an electric field is defined as the work done in bringing a unit positive charge from infinity to that point. An alternative definition is that it is the potential energy of a unit positive charge placed at that point with the zero being at infinity The electric potential (VE) is given by the equation: Electrostatic potential: VE = (1/4εo)Q/d The unit of electrostatic potential is the volt (V). The variation of potential with distance from a charge Q is shown in Figure 1. +Q Figure 1 d P +q Infinity (∞) If a charge q is in the field then its potential energy is given by : Electrostatic potential energy = qVE= (1/4εo)qQ/d and this is measured in joules. When one positive charge moves away from another positive charge its potential energy is decreased but when a negative charge is moved away from a positive charge (e.g. electron and proton) its potential energy increases. 1 The variation of potential energy with distance is shown in Figure 2. Potential energy 16 8 4 2 2 4 8 16 Distance Figure 2 Example problems 1. Calculate the charge that produces a potential of 12 V at a distance of 0.1 nm in a vacuum. Using: VE= (1/4πεo)Q/d Q = VEd/(1/4πεo) = 10.8 C 2. Calculate the force on a charge of 3x10-5C placed in a field of strength 250 Vm -1. Force = EQ = 3x10-5 x 250 = 7.5 x10-3 N. 3. Calculate the potential energy of a charge of 10-9 C placed 0.1nm from a charge of 3 C. Potential energy = (1/4πεo)Qq/d = 9x10-9x10-9x3/10-10= 2.7 x10 –7 J 2