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Advanced Higher Physics

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 -

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Advanced Higher Physics

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  1. Advanced Higher Physics Electric Potential

  2. 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)

  3. d A B 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. ( also, * This is only true for a UNIFORM field. )

  4. 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 3

  5. 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,

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

  7. Electric Potential 6 • Integrating as shown, we get

  8. 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.

  9. 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 -

  10. Electric Potential 9 • Unlike the electric field, the electric potential around a point charge decays as 1 / r , not 1 / r2. • The potential is a scalar quantity, not a vector quantity, although its sign is determined by the sign of the charge Q.

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

  12. 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. Electric Potential 11

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