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Understanding Electric Potential in Charged Conductors

Learn about electric potential, potential difference, conductors in equilibrium, and applications of electrostatics in this comprehensive guide. Explore concepts like equipotential surfaces, irregularly shaped conductors, and the Millikan Oil Drop Experiment. Dive into practical applications like the Van de Graaff Generator and Electrostatic Precipitator in industries like xerography.

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Understanding Electric Potential in Charged Conductors

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  1. -Electric Potential due to a Charged Conductor-The Millikan Oil Drop Experiment-Applications of Electrostatics AP Physics C Mrs. Coyle

  2. Electric Potential –What we used so far! • Electric Potential • Potential Difference • Potential for a point charge • Potential for multiple point charges • Potential for continuous charge distribution

  3. Is the surface of a charged conductor an equipotential? • Is the electric potential constant everywhere inside a charged conductor and equal to its value at the surface?

  4. Electric Potential Difference on the Surface of a Charged Conductor in Equilibrium • Let A and B be points on the surface of the charged conductor • Let ds be the displacement from A to B. • E is always perpendicular to the displacement ds. So, E ·ds = 0 • Therefore, the potential difference between A and B is also zero

  5. Electric Potential Difference on the Surface of a Charged Conductor in Equilibrium • V is constant everywhere on the surface of a charged conductor in equilibrium • ΔV = 0 between any two points on the surface • The surface of any charged conductor in electrostatic equilibrium is an equipotential surface

  6. What about the inside of a charged conductor? • E=0 inside the conductor in equilibrium • E ·ds = 0 • Therefore, the electric potential is constant everywhere inside the conductor and equal to the value at the surface.

  7. Solid Conducting Sphere • r<R V=kq/R E=0 • r=R V=kq/R E=kQ/R2 • r>R V=kq/r E=kQ/r2 Note: • V is a Scalar related to energy • E is a Vector related to force.

  8. Irregularly Shaped Conductors • The charge density is high where the radius of curvature is small • The electric field is high at sharp points

  9. Irregularly Shaped Conductors • The field lines are perpendicular to the conducting surface • The equipotential surfaces are perpendicular to the field lines

  10. Quick Quiz 25.10 Draw a graph of the electric potential as a function of position relative to the center of the left sphere. (Left sphere 1, radius a),(Right sphere 2, radius c) The centers of the spheres are a distance b apart.

  11. Quick Quiz 25.10 Answer: See below. Notice the flat plateaus at each conductor, representing the constant electric potential inside a solid conductor.

  12. Ex 25.9: Two Connected Charged Spheres • The separation distance of the spheres is much greater than the radius of either sphere so their fields do not affect each other. • Show

  13. ΔV= O in a Cavity in a Conductor, so Equipotential to Body of Conductor • Assume no charges are inside the cavity • E=0 inside the conductor • The electric field inside does not depend on the charge distribution on the outside surface of the conductor

  14. Corona Discharge • If the electric field near a conductor is sufficiently strong, electrons resulting from random ionizations of air molecules near the conductor accelerate away from their parent molecules • These electrons can ionize additional molecules near the conductor

  15. Corona Discharge • The glow that is observed near a charged conductor of a strong E-field. • It results from the recombination of freed electrons with the ionized air molecules • Most likely to occur near very sharp points

  16. Millikan Oil-Drop Experiment

  17. Millikan Oil-Drop Experiment • Robert Millikan measured e, the charge of the electron e = 1.60 x 10-19 C • He also demonstrated the quantized nature of this charge

  18. Oil-Drop Experiment • With no electric field between the plates: The drop reaches terminal velocity with FD = mg

  19. Oil-Drop Experiment • When an electric field is set up between the plates the drop moves upwards and reaches a new terminal velocity • Fe = mg +FD =qE • Solve for q • Observed thousands of times and always found e=multiple of 1.6x10-19 C

  20. Van de Graaff Generator

  21. Electrostatic PrecipitatorOn Off

  22. Electrostatic Precipitator • It removes particulate matter like ashes from combustion gases • Corona discharge ionizes particles of air • Most of the dirt particles are negatively charged and are drawn to the walls by the electric field of the negative potential coil.

  23. Xerography: uses photoconductive material coating(Selenium) a drum

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