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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 = (1/4εo)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= (1/4εo)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
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