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Electric Field and Potential: Metal Spheres & Charge Distribution Problem

Explore charge distribution problems with metal spheres, Gauss's Law applications, and electric field calculations. Solve practice questions to understand electric potential and field generated by various configurations. Prepare for upcoming quiz and lab sessions.

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Electric Field and Potential: Metal Spheres & Charge Distribution Problem

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  1. Agenda • Today • Problems in Last Few Chapters • Tomorrow • Quiz on 21-23, Lab • Wed • Shand begins 25

  2. Charge Distribution: Conducting Donut Point Charge Outside on Left Which is correct? Why?

  3. How to Solve this ProblemPractice Ch. 22 What is Electric Field Produced by This? Sphere Hole in Sphere Constant charge density R2 R1 Hole Located at x=-R1/2 R2 = R1/8 Charge Density = r

  4. How to Create a hole? Simpler way to look at this? R2 R1 Hole Located at x=-R1/2 R2 = R1/8 Charge Density = r

  5. R2 R1 How to Create a hole? Simpler way to look at this? Hole Located at x=-R1/2 R2 = R1/8 Charge Density = r

  6. How to Create a hole? Make two spheres One +r & one –r Superposition [Add together] r = - r = + R2 R1 Hole Located at x=-R1/2 R2 = R1/8 Charge Density = r Try This?

  7. Electric Field & Potential Two Metal Spheres Concentric Outer Hollow Iner: Charged +Q Outer: Charged -Q R3 R2 R1

  8. Electric Field & PotentialEverywhere? Two Metal Spheres Concentric Outer Hollow Iner: Charged +Q Outer: Charged -Q R3 R2 R1 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity

  9. Electric Field & Potential Two Metal Spheres Concentric Outer Hollow Iner: Charged +Q Outer: Charged -Q R3 R2 R1 Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity

  10. Electric Field & Potential -Q Where is charge located? R3 R2 R1 +Q Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity

  11. Metals: E = 0 Inside Metal -Q Where is charge located? - - R3 - - - - R2 - + + - - - + + - +Q + R1 - Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity - + - + - - - - - - - -

  12. Metals: E = 0 Inside Metal -Q Gauss’s Law Field =0 if QENCL=0 Charges on Outer Surface - - R3 - - - - R2 - + + - - - + + - +Q + R1 - Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity - + - + - - - - - - - -

  13. Electric Field? Specific Regions 0 <r <R1: E = ? R1 < r < R2: E=? R2 < r < R3: E = ? R3 < r < Infinity: E = ? -Q - - R3 - - - - R2 - + + - - - + + - +Q + R1 - - + - + - - - - - - - -

  14. Electric Field? Specific Regions 0 <r <R1: E = 0 R1 < r < R2: E=? R2 < r < R3: E = 0 R3 < r < Infinity: E = 0 -Q - - R3 - - - - R2 - + + - - - + + - +Q + R1 - - + - + - - - - - - - -

  15. Electric Field? Specific Regions 0 <r <R1: E = 0 R1 < r < R2: E = kQ/r2 R2 < r < R3: E = 0 R3 < r < Infinity: E = 0 -Q - - R3 - - - - R2 - + + - - - + + - +Q + R1 - - + - + - - - - - - - -

  16. Potential First: Reference Point -Q Gauss’s Law Field =0 if QENCL=0 Charges on Outer Surface - - R3 - - - - R2 - + + - - - + + - +Q + R1 - Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity - + - + - - - - - - - -

  17. Potential: Reference Point -Q V at infinity = 0 (3D ref) E in metal = 0 E outside: kQENCL/r2 - - R3 - - - - R2 - + + - - - + + - +Q + R1 - Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity - + - + - - - - - - - -

  18. Potential: Reference PointStart at r=infinity, work way in -Q V at infinity = 0 (3D ref) E in metal = 0 E outside: kQENCL/r2 - - R3 - - - - R2 - + + - - - + + - +Q + R1 - Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity - + - + - - - - - - - -

  19. Where is V =0?Where is V= Constant?Try this? Capacitance? (C=Q/V) -Q V at infinity = 0 (3D ref) E in metal = 0 E outside: kQENCL/r2 - - R3 - - - - R2 - + + - - - + + - +Q + R1 - Specific Regions 0 <r <R1 R1 < r < R2 R2 < r < R3 R3 < r < Infinity - + - + - - - - - - - -

  20. Agenda • Today • Problems in Last Few Chapters • Tomorrow • Quiz on 21-23, Lab • Wed • Shand begins 25

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