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PHYSICS 51 lecture 23.1

PHYSICS 51 lecture 23.1. RICHARD CRAIG. Plan for the day. Basic ideas on Potential Analogy to topographic map Calculations of Potentials Point charge Collection of points Distribution of charge Metal ball Electrostatic potential energy calculation. Misc. Items. HW #4

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PHYSICS 51 lecture 23.1

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  1. PHYSICS 51 lecture 23.1 RICHARD CRAIG

  2. Plan for the day • Basic ideas on Potential • Analogy to topographic map • Calculations of Potentials • Point charge • Collection of points • Distribution of charge • Metal ball • Electrostatic potential energy calculation

  3. Misc. Items • HW #4 • Chapter 23 Exercises: #4, #28, #39, #62 • Due next Tuesday, Feb 18

  4. What is a Volt • Batteries range from 1.5V to 12V • What is the difference • By the way what is a volt?

  5. What is a Volt? • A unit of electrical energy 2) A unit of electrical capacity • 3) A unit of electrical energy per unit charge 4) A unit of electrical power

  6. Electric Potential • Formal Defintion

  7. Potential (Electric) Misc. Facts • Vab is the work done by the electric force per unit charge to move from point a to point b • A Scalar Field (not a vector!) • Defined with respect to a reference potential (often V=0 at infinity) • The electric field is the negative gradient of the potential • Simple 1-D: E= -(dV/dx)i

  8. ELECTRIC FIELD LINES PERPENDICULAR TO EQUIPOTENTIAL LINES In Lab #1 you will use a voltmeter to measure the equipotential lines (in Volts) in order to determine the magnitude and direction of the electric field lines.

  9. Topographical Maps, Potential, and Electric fields • The analogy between potential energy due to height and electric Potential is quite good • Equal potential surface is constant height • Magnitude of field is rate of change of potential (steepness)

  10. Calculating Potential • Single point charge +Q • V = kQ/r (k=1/40) • Collection of point charges • V = kQi/ri • Continuous Charge • dV = kdQ/r

  11. Potential due to point charge • What is the potential due a point charge +q a distance r away • Two point charges

  12. Example: Conducting Sphere • A solid conducting ball of radius R has a charge +Q. • Where is the charge • What is the Electric field outside the sphere • What is the Potential outside the sphere • What is the Electric Field inside the sphere • What is the Potential inside the sphere

  13. Potential and Field from Charged conducting ball

  14. Example of Potential due to distributed charge A thin wire with total charge +Q is bent into a Quarter circle. What is the Potential at the center of the circle

  15. Potential and Potential Energy • Analogy to Electric force and field • Electric Force is interaction between two charges or one charge and a field • Electric Field can be due to a single charge • Electric potential can be due to a single charge • Electric potential energy is the energy associated with taking a charge through a potential

  16. Graphs of the potential energy U of two point charges q and q0 versus their separation r.

  17. Example: calculation with Electric Potential Energy A proton is shot at the nucleus of gold atom with and velocity of 1.0 x 106m/s. If shot exactly straight on (1-D problem) how close will it get?

  18. Potential (Electric) Misc. Facts • Vab is the work done by the electric force per unit charge to move from point a to point b • A Scalar Field (not a vector!) • Defined with respect to a reference potential (often V=0 at infinity) • The electric field is the negative gradient of the potential • Simple 1-D: E= -(dV/dx)i

  19. Calculating Potential • Single point charge +Q • V = kQ/r (k=1/40) • Collection of point charges • V = kQi/ri • Continuous Charge • dV = kdQ/r

  20. Example: Conducting Sphere • A solid conducting ball of radius R has a charge +Q. • Where is the charge • What is the Electric field outside the sphere • What is the Potential outside the sphere • What is the Electric Field inside the sphere • What is the Potential inside the sphere

  21. Potential and Field from Charged conducting ball

  22. Example of Potential due to distributed charge A thin wire with total charge +Q is bent into a Quarter circle. What is the field at the center of the circle What is the Potential at the center of the circle

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