1. P06 - 1 Class 06: Outline Hour 1: Electric Potential Hour 2: Expt. 3: Signal Generator

2. P06 - 2 Last Time: Kelvin Water Dropper Definition of Potential

3. P06 - 3 Kelvin Water Dropper This device separates an ever increasing amount of positive and negative charge until we get a spark across the gap at the bottom. How?

4. P06 - 4 PRS Questions: How Does The Water Dropper Work?

5. P06 - 5 Potential & Energy Work done to move q from A to B: Joules Units: Joules/Coulomb = Volts

6. P06 - 6 Potential Of Point Charge Take V = 0 at r = ∞:

7. P06 - 7 Potential in Uniform Fields

8. P06 - 8 PRS Question: Point Charge Potential

9. P06 - 9 Potential Landscape Negative Charge Positive Charge

10. P06 - 10 Deriving E from V

11. P06 - 11 Deriving E from V A = (x,y,z), B=(x+  x,y,z) E x = Rate of change in V with y and z held constant

12. P06 - 12 Deriving E from V In three dimensions: which implies

13. P06 - 13 Introducing the gradient (del) operator: Then E is: Deriving E from V

14. P06 - 14 Equipotentials

15. P06 - 15 Topographic Maps

16. P06 - 16 Equipotential Curves All points on equipotential curve are at same potential. Each curve represented by V(x,y) = constant

17. P06 - 17 Direction of Electric Field E E is perpendicular to all equipotentials Constant E fieldPoint ChargeElectric dipole

18. P06 - 18 Properties of Equipotentials E field lines point from high to low potential E field lines perpendicular to equipotentials Have no component along equipotential No work to move along equipotential

19. P06 - 19 Introduction to Experiment #3: Signal Generator Introduction to instrumentation requiring a look ahead at physics

20. P06 - 20 Ohm’s Law: Voltage & Current Voltages can be constant (battery) or time dependent (AC power) Charges want to move – current (C/s) Motion restricted – resistance (Ohms) V = I R It takes energy to move charges: P = V I (J/C C/s = J/s = Watts)

21. P06 - 21 Experiment #3: Signal Generator

22. P06 - 22 Continuous Charge Distributions

23. P06 - 23 Electric Potential from Continuous Charge Distribution Continuous charge distribution: Potential at P is found by summing over all dq Scalar not Vector

24. P06 - 24 Group Problem: Ring of Charge P on axis of ring of charge, x from center Radius R, total charge Q (evenly distributed) Find V at P. Then derive E from V. R

25. P06 - 25 Configuration Energy

26. P06 - 26 Configuration Energy How much energy to put two charges as pictured? 1)First charge is free 2)Second charge sees first:

27. P06 - 27 Configuration Energy How much energy to put three charges as pictured? 1)Know how to do first two 2)Bring in third: Total configuration energy: