Class Activities Potential slide 2 Today Voltage or Electric Potential The 1120 version Voltage V kq r from a point charge Voltage potential energycharge D V is path independent ID: 1001250
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1. POTENTIAL
2. Class Activities: Potential (slide 1)
3. Class Activities: Potential (slide 2)
4. Today: Voltage or “Electric Potential”The 1120 version:Voltage V = kq/r from a point chargeVoltage = potential energy/chargeDV is “path independent”E = -dV/dr
5. Potential and E-field= external work done on charge to move it
6. Potential and E-fieldThe fact that V is well defined arises fromWhich is exactly the same as (!)
7. Potential and E-fieldOne way to find V(r) (given charges):
8. One way to find V(r) (given charges):Voltage V = kq/r from a point charge !
9. So, what doesHave to do with And why is that the same as
10. Divergence theorem:Stoke’s (or “curl”) theorem:Fundamental theorem:
11. Common vortex
12. Feline Vortex
13. What is the curl of this vector field, Vin the region shown below?non-zero everywhereZero at some points, non-zero otherszero curl everywhere shown1.8
14. What is the curl of this vector field, Vin the region shown below?non-zero everywhereZero at some points, non-zero otherszero curl everywhere shown1.8
15. What is the curl of this vector field, Vin the region shown below?1.8
16. Why is
17. 1.80!
18. What is the curl of this vector field, in the red region shown below?non-zero everywhere in the boxNon-zero at a limited set of pointszero curl everywhere shownWe need a formula to decide for sure 1.8
19. What is the curl of this vector field, in the red region shown below?non-zero everywhere in the boxNon-zero at a limited set of pointszero curl everywhere shown1.8
20. What is the curl of this vector field, in the red region shown below?non-zero everywhere in the boxNon-zero at a limited set of pointszero curl everywhere shown1.8
21. Which of the following could be a static physical E-field in a small region?III Only I B) Only II C) Both D) NeitherE) Cannot answer without further info2.43b/1.7b
22.
23. (with )It is also true thatwhere
24. (with )It is also true thatwhere
25. (with )It is also true thatwhere Yes B) No C) ???Question: is the following mathematically ok?
26.
27. A) Sure, why not?B) No wayC) Not enough info to decideCould the following electrostatic field possibly exist in a finite region of space that contains no charges? (A, and c are constants with appropriate units) 2.43
28. A)B) C) D) Which of the following electrostatic fields could exist in a finite region of space that contains no charges?2.43None of these
29. Given a sphere with uniform surface charge density what can you say about the potential V inside this sphere? (Assume as usual, V(∞)=0) V=0 everywhere inside V = non-zero constant everywhere insideC) V must vary with position, but is zero at the center.D) None of these. 2.45
30. Why is in electrostatics? Because Because E is a conservative field Because the potential between two points is independent of the path All of the above NONE of the above - it's not true!
31. A uniformly charged ring, in the xy plane, centered on the origin, has radius a and total charge Q. V(r =) = 0. What is the voltage at z on the z-axis?az
32. A uniformly charged ring, in the xy plane, centered on the origin, has radius a and total charge Q. V(r =) = 0. What is the voltage at z on the z-axis?azdq
33. Summary:Def of potential:How do you compute it:What good is it?Where did it come from? Which by Stoke’s theorem is mathematically equivalent to:
34. TutorialPlease click the letter below when you START working on the following parts:I’m now starting (click right away!)I’m starting iiI’m starting iiiI’m starting the 2nd pageDONE!
35. TutorialWhen you are DONE, click in:What is the slope of V(r) at the origin?PositiveNegativeZeroIt depends!Be prepared to explain/defend your answer!
36. A spherical shell has a uniform positive charge density on its surface. (There are no other charges around)A: E=0 everywhere insideB: E is non-zero everywhere in the sphere C: E=0 only at the very center, but non-zero elsewhere inside the sphere.D: Not enough info givenWhat is the electric field inside the sphere?2.26
37. A) Could be E(r), or V(r)B) Could be E(r), but can't be V(r)C) Can't be E(r), could be V(r)D) Can't be either E) ???Could this be a plot of |E|(r)? Or V(r)? (for SOME physical situation?)2.44
38. The voltage is zero at a point in space. You can conclude that :The E-field is zero at that point. B) The E-field is non-zero at that pointC) You can conclude nothing at all about the E-field at that point
39. You can conclude that :A) The E-field has constant magnitude along that line.B) The E-field is zero along that line.C) You can conclude nothing at all about the magnitude of E along that line.V=constantThe voltage is constant everywhere along a line in space.
40. xyIn spherical coordinates, the correct expression for dL is:Consider an infinitesimal path element dL directed radially inward, toward the origin as shown.
41. Given a spherical SHELL with uniform surface charge density (no other charges anywhere else) what can you say about the potential V inside this sphere? (Assume as usual, V(∞)=0) V=0 everywhere inside V = non-zero constant everywhere insideC) V must vary with position, but is zero at the center.D) Could be A OR B!E) None of these, it’s something else! 2.45
42. We usually choose V(r ∞) ≡ 0 when calculating the potential of a point charge to be V(r) = +κq/r. How does the potential V(r) change if we choose our reference point to be V(R)=0 where R is closer to +q than r. A V(r) is positive but smaller than kq/rB V(r) is positive but larger than kq/rC V(r) is negativeD V(r) doesn’t change (V is independent of choice of reference)+qRr∞SC-4
43. Two isolated spherical shells of charge, labeled A and B, are far apart and each has charge Q. Sphere B is bigger than sphere A. Which shell has higher voltage? [V(r=) = 0]A) Sphere A B) Sphere B C) Both have same voltage.+Q+QAB
44. Why is in electrostatics? Because Because E is a conservative field Because the potential (voltage) between two points is independent of the path All of the above NONE of the above - it's not true!2.46
45. A parallel plate capacitor is attached to a battery which maintains a constant voltage difference V between the capacitor plates. While the battery is attached, the plates are pulled apart. The electrostatic energy stored in the capacitor A) increases B) decreases C) stays constant.V