Electrical Potential January 28 th , 2013

1. Electrical PotentialJanuary 28th, 2013 Chapter 18 • Electric potential energy • Electric potential or Voltage • Equipotential surfaces

2. Electric Potential Energy Given 2 point charges q1 and q2 They exert a force on each other. If the separation between them changes, e.g. decreases in the figure below, the electric force does work.

3. Electric Force

4. Electric Potential Energy

5. Electric Potential Energy

6. Electric and Gravitational Potential Energy • Both vary as 1/r • The electric potential energy falls to zero when the separation between two charges is infinite • The gravitational potential energy falls to zero when the separation between two masses is infinite

7. Electric Potential or Potential or Voltage • Electric potential energy is a property of a system of charges or of a charge in an electric field • It is not a property of a single charge, alone Units are Volts; 1 V = 1 J/C = 1 Nm/C

8. Electric Field units are V/m The electric field may vary with position The magnitude and direction of the electric field are related to how the electric potential changes with position ΔV = -E Δx or

9. Electronvolt • Often we are concerned with the energy gained or lost as an electron or ion moves through a potential difference • It is convenient to introduce a unit of energy called the electronvolt(eV) • One electron volt is defined as the amount of energy gained or lost when an electron travels through a potential difference of 1 V 1 eV = 1.60 x 10-19 J

10. Electric Potential due to a point charge + - key chart: use this! The electric potential at a distance r away from a single point charge q is given by The solid curve shows V(r) for a positive charge, the dotted line V(r) for a negative charge

11. Changes in Potential • Since changes in potential (and potential energy) are important, a “reference point” must be defined • The standard convention is to choose V = 0 at r = ∞ • In many problems, the Earth may be taken as V = 0 • This is the origin of the term electric ground • The convention is that ground is where V = 0 + -

12. Electric field near a charged metal sphere • E=0, V=const inside the metal sphere • E decreases rapidly, V decreases more slowly away from the sphere

13. Problem 18.20 in book A proton moves from a location where V= 75V to one where V=-20V. (a) What is the change in the proton’s kinetic energy? (b) If we replace the proton with an electron, what is the change in kinetic energy?

14. Problem 18.20 in book A proton moves from a location where V= 75V to one where V=-10V. (a) What is the change in the proton’s kinetic energy? (b) If we replace the proton with an electron, what is the change in kinetic energy? Think: The potential energy of a charge changes when it moves from one point to another point of different electric potential. The kinetic energy will also change as a result, in accordance with the total energy conservation. There is no external energy feeding into the system here, nor any energy dissipation, therefore the sum of the potential energy and kinetic energy should be a constant. The change in kinetic energy will be equal in magnitude and opposite in sign to the change in potential energy.

16. Equipotential lines • A useful way to visualize electric fields is through plots of equipotential lines • Along these lines the electric potential is constant. The electric field at every point of the equipotential lines is perpendicular to the lines. • Equipotential lines are in two-dimensions

17. Hair segments in E-field on document camera hair segments align with E-field equipotentials

18. Equipotential surfaces • A useful way to visualize electric fields is through plots of equipotential surfaces • Contours where the electric potential is constant • Equipotential lines are in two-dimensions • In B, several surfaces are shown at constant potentials

19. Equipotential surfaces • Equipotential surfaces are always perpendicular to the direction of the electric field (due to the relationship between E and V: E = -DV/Dx) • For motion parallel to an equipotential surface, V is constant and ΔV = 0 • The electric field component parallel to the surface is zero

20. Equipotential Surface – Point Charge • The electric field lines emanate radially outward from the charge • The equipotential surfaces are perpendicular to the field • The equipotential surfaces are a series of concentric spheres • Different spheres correspond to different values of V

21. Equipotential Surface – wire

22. Equipotential Surface – solid shape

24. Biological Applications • In the 1790’s Luigi Galvani (Italian, 1737-1798) showed that nerves and muscles used electrical potential

25. Biological Applications • A defibrillator uses an externally applied potential to shock the heart into normal beating

26. Biological Applications • En electrocardiogram (ECG or EKG) monitors potential at various points in the chest to show heart movements

27. Biological Applications • An electroencephalogram (EEG) detects potentials in the brain

28. Lightning Rod • The figure gives a sketch of the electric field near a lightning rod • The field lines are perpendicular to the surface of the metal rod • The field lines are largest near the sharp tip of the rod and smaller near the flat side

29. Lightning Rod Model • A lightning rod can be modeled as two metal spheres connected by a metal wire • The smaller sphere represents the rod tip, the larger sphere represents the flatter rod body

30. Lightning Rod Analysis • The two spheres two have the same potential • The charges are related by • Thus • The field is large near the surface of the smaller sphere • This means that the field is largest near the sharp edges of the lightning rod