1 CHAPTER 23 ELECTRIC POTENTIAL BASIC CONCEPTS: ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL ELECTRIC POTENTIAL GRADIENT – POTENTIAL DIFFERENCE 2 POTENTIAL ENERGY h PE = U = mgh PE KE Or U K And U + K = total energy = constant 3 BOOK EXAMPLE 4 Charged Particle in Electric Field is similar 5 Consider a point charge q that sets up an electric field in space 6 Now a test charge q0 is placed at position a a distance ra from q0. Then q0 moves to position b a distance rb from q0. What is the change in potential energy? The change in potential energy is the negative of the work done to move the test charge from a to b. The force on the test charge is  7 The work done is force times distance. But the force changes as q0 moves away from q Must integrate Use  Then        8 The change in potential energy, is the negative of this work.     DEFINITION: ELECTRICAL POTENTIAL IS POTENTIAL ENERGY PER UNIT CHARGE 9 Therefore divide all terms by     Thus         10 Now consider the same situation 11 We have as we did at the beginning The change in potential energy, is the negative of this work. Therefore    In Chapter 21 we defined the Electric Field as the force per unit charge  12 And we have  Divide all terms by q0     13 POTENTIAL AT A POINT Once again look at this situation We have 14   Just like in potential energy of the particle on a hill we can choose the potential energy and therefore the potential to be zero at any arbitrary point. Choose infinity In the figure When   15 Then   From Chapter 21  Therefore   16       Choose  where      17 The potential at any point in space a distance from a charge will be  POTENTIALS ADD (SCALERS) Just as we did with the electric field we can add the potentials for many charges in an area. 18 EXAMPLE A 60cm 30cm   50µC ‐50 µC What is the potential at A?       19 Example 23.11 Potential on axis of ring of charge. Choose small segment of ring that has charge . The segment is a distance form point P. Then    20 Integrate to get V   Everything is constant except     21 Use the result to find potential on axis of disk of charge. This is diagram for E but use it for finding potential at P For ring of radius contribution to V is   22 Disk is made up of rings each with area Charge density of disk is total charge divided by total area   Therefore   23     Integrate   24   For the disk   25 TWO MORE BASIC PIECES OF INFORMATION If we know V we can find E    26 Example In this chapter we found for ring of charge   In chapter 21 we found for ring of charge   Use equation above for V to find  27         28 ELECTRON VOLT An electron volt is a unit for energy. It is the work necessary to move an electron (charge ) a potential difference of 1 volt. 1 Volt Batt The work to move a charge across a potential difference is 29  Therefore 