Advanced Higher Physics Electric Potential

Electric Potential 1 V = work done / q(measured in J C -1 ) Defined as ‘the work done per unit positive charge in moving a charge from infinity to a point in an electrical field’ Gives the definition of the volt - one volt (1 V) = one joule per coulomb (1 JC -1 )

Electric Potential 2 The potential difference (p.d.) between two points A and B is the work done per unit charge in moving between points A and B. d B A ( also, * This is only true for a UNIFORM field. )

Electric Potential 3 Law of conservation of energy tells us that work done in moving charge from point A to point B is independent of the route taken. If the p.d. between A and B is V, the same amount of work must be done in moving a unit of charge from A to B, whatever path is taken. This is because the electric field is a conservative field.

Electric Potential 4 From the equation E = V / d we can see that electrical field strength, E, can be expressed volts per metre, V m -1 E can be thought of as a ‘potential gradient’ In a non-uniform field,

Electric Potential 5 using r to represent distance, But, we already know that - Combining these gives -

Electric Potential 6 Integrating as shown, we get

Electric Potential 7 NB - be careful with the sign of the potential. In moving a positive charge from infinity to r, the charge will have gained potential energy, as work has to be done on the charge against the electric field.

Electric Potential 8 So if we have defined the potential to be zero at infinity, the potential V must be positive for all r less than infinity. Thus the potential at r is given by -

Electric Potential 9 Unlike the electric field, the electric potential around a point charge decays as 1 / r, not 1 / r 2. The potential is a scalar quantity, not a vector quantity, although its sign is determined by the sign of the charge Q.

Electric Potential 10 The field strength and potential around a positive point charge are plotted below

Electric Potential 11 We can plot the equipotential lines (connecting points of the same potential) around a point charge, as shown below The equipotentials form a set of concentric spheres around the charge Note that the equipotentials cut the electric field lines at right angles. There is no work done in moving a charged particle along an equipotential.