1. Electric Potential Physics 102 Professor Lee Carkner Lecture 12

2. PAL #11 Electric Field  Electric field between charge +3q and charge -1q  Ratio of lines touching 3q to lines touching -1q must be 3 to 1   At large distance away acts as net charge of +2q 

3. PAL #11 Electric Field  To find electric field at a point between the charges:  E =  “q” for the charges is e = 1.6X10 -19 C,  3q = (3)(1.6X10 -19 ) = 4.8X10 -19 C  1q = (1)(1.6X10 -19 ) = 1.6X10 -19 C   Find E from the 3q charge, find E from the 1q charge  Since both fields point the same way (to the right), add them up

4. The above electric field, A)increases to the right B)increases to the left C)increases up D)increases down E)is uniform

5. Is it possible to have a zero electric field on a line connecting two positive charges? A)Yes, at one point on the line B)Yes, along the entire line C)No, the electric field must always be greater than zero D)No, but it would be possible for two negative charges E)No, the electric field is only zero at large distances

6. A hollow block of metal is placed in a uniform electric field pointing straight up. What is true about the field inside the block and the charge on its top surface? A)Field inside points up, charge on top is positive B)Field inside points down, charge on top is negative C)Field inside points up, charge on top is zero D)Field inside is zero, charge on top is positive E)Field inside is zero, charge on top is zero

7. Electrical Force and Energy  Like any other force, the electrical force can do work:  If a force does work, the potential energy must decrease  e.g.  Decrease in PE (  PE) equal to the work  PE = -W = -qEd   We would like to define a quantity that tells us about the electrical energy at a point in the field that does not depend on the test charge

8. Potential Difference  The potential difference (  V) between two points is the difference in electrical potential energy between the two points per unit charge:  V = V f - V i =  PE/q   For any given point with potential V   Potential is the potential energy per unit charge   Potential given in volts (joules/coulomb)  1V = 1 J/C

9. Potential Confusion  The potential and the potential energy are two different things   Potential at a point is the same no mater what kind of test charge is put there   e.g. V = 12 V (potential is equal to 12 volts)

10. Signs  As a positive charge moves along the electric field, the particle gains kinetic energy and the field loses potential and potential energy   The potential energy lost by the field goes into work  Since energy must be conserved:   An electric field will naturally move a positive particle along the field lines, doing positive work and resulting in a decrease in potential and potential energy  n.b.

11. E +  Down    field does work ““  Up   gain PE   field “does” negative work   For negative particle, everything is backwards

12. Work  We will talk of work done by the system and work done on the system  Work done by the system is positive if it decreases the potential energy   Work done by the system is negative if it increases the potential energy   The negative work done by the system is the positive work done on the system

13. Today’s PAL  Consider 4 situations: + charge moves with E field, + charge moves against E field, - charge moves with E field, - charge moves against E field  For each situation:  What is the sign of the change in potential energy?  What is the sign of the potential difference (final-initial)?  What is the sign of the work done by the system?  Does this happen naturally?

14. Work and Potential   Positive work done by the electric force reduces potential energy (W = -  PE)  We can also write work as  If there is no potential difference there is no work done by the electric force 

15. Potential and Energy  We can convert potential energy into kinetic energy  As a particle moves from an initial to a final position, energy is conserved:   Since PE = Vq  KE f = KE i + qV i -q V f   Thus if you go from high to low potential (“downhill”) the particle speeds up 

16. Conductors   All points on the surface must be at the same potential   Since there is no field inside the conductor, the electric potential is constant inside the conductor

17. Equipotentials  Equipotentials lines are drawn perpendicular to the electric field   The equipotentials for a single point charge are a series of concentric circles   Equipotentials cannot cross  This would mean the same point had two values for V

18. Point Charges and Potential  Consider a point charge q, what is the potential for the area around it?   At infinity the potential is zero   It can be shown that: V = k e q / r  For a single point charge

19. Potential Energy and Two Charges  Since the potential energy is just qV, for two point charges:  The electrical energy of the situation depends on how far apart they are and their charge  Example: two positive charges brought close together have an increase in potential energy

20. Finding Potential   Potential is a scalar (not a vector) and so can be found by summing the magnitudes of the potentials from each charge  Total V = V 1 + V 2 + V 3 … 

21. Next Time  Read Ch 17.7-17.9  Homework, Ch 17: P 10, 16, 35, 46