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Understanding Equipotential Lines and Electric Field Relationships

Explore the quantitative relation between equipotential lines and the electric field, visualizing field lines as topographic maps to understand their direction and magnitude. Learn about conductors, dielectric strength, capacitance, and parallel-plate capacitors.

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Understanding Equipotential Lines and Electric Field Relationships

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  1. Hint on Prob. 17.16:

  2. Equipotential and field lines:

  3. Equipotential lines field lines:

  4. Equipotential lines and the Electric field: Quantitative relation

  5. Equipotential lines and the Electric field: Quantitative relation ?

  6. Equipotential lines and the Electric field: Quantitative relation

  7. Small enough scale, looks like parallel plate field:

  8. Small enough scale, looks like parallel plate field: (calculate)

  9. Formally: Direction: downhill

  10. Pretending that V(x) is like a topographic map: The Electric field always points in the direction of steepest descent! B) The magnitude of the electric field is given by the slope in that direction! alternate units for E: V/m

  11. Note: color Scheme is backward

  12. Example 17.22 where’s V = 0? 5 cm Two possibilities!

  13. Example 17.22 where’s V = 0? Possibility #1 5 cm x

  14. Example 17.22 where’s V = 0? Possibility #2 x

  15. Conductors!

  16. Electric fields just outside of a conductor are strong where the conductor is pointy: Dielectric strength of a material = maximum electric field the Material can stand before breaking down. Dielectric strength of air = 3 × 106 V/m Example: Voltage of a 8 cm spark!

  17. Capacitance:

  18. Capacitance: Must be at different potentials!

  19. Capacitance:

  20. Capacitance:

  21. 10 cm Parallel-plate capacitor: 10 cm 0.1 cm Square plates

  22. Parallel-plate capacitor: Q = ?

  23. Parallel-plate capacitor: Dielectric constant! Quartz: k = 4.3 Dielectric! 10 cm 0.1 cm Square plates

  24. V de G demo again, big and little spheres – spark size Leyden-jar demo

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