W9_parallel_resonance.eps
Week 1: Discrete Charge and the Electrostatic Field 59 Problem 9. −q +q E −q +q E top view side view θ Suppose you have a “dumbb ...
60 Week 1: Discrete Charge and the Electrostatic Field Problem 10. r = d/2 −e +e v v An electron (charge−e, massm) and a positro ...
Week 1: Discrete Charge and the Electrostatic Field 61 Advanced Problem 11. +Q +q,m A small (point) massm, which carries a charg ...
62 Week 2: Continuous Charge and Gauss’s Law Advanced Problem 12. +Q −q,m L x A small bead of massmand carrying a negative charg ...
Week 2: Continuous Charge and Gauss’s Law Continuous Charge Charge distributions can often be continuous. We therefore define t ...
64 Week 2: Continuous Charge and Gauss’s Law Gauss’s Law for the Electric Field Gauss’s Law is written: ∮ S/V E~·nˆdA= 4πk ∫ V ...
Week 2: Continuous Charge and Gauss’s Law 65 Now we can sum over a lotfewerobjects. There aren’t as many blocks a micron in size ...
66 Week 2: Continuous Charge and Gauss’s Law We used charge per unit volume in this discussion, but we will find that charge oft ...
Week 2: Continuous Charge and Gauss’s Law 67 Example 2.1.1: Circular Loop of Charge dθ dE r dEz z a dl = a dθ φ λ x y z Figure 1 ...
68 Week 2: Continuous Charge and Gauss’s Law In these equations, we must evaluate sinφand cosφusing the right triangleazr: sinφ ...
Week 2: Continuous Charge and Gauss’s Law 69 Example 2.1.2: Long Straight Line of Charge dx θ dEx dEy dE y r x λ x y θ P Figure ...
70 Week 2: Continuous Charge and Gauss’s Law so dx= y dθ cos^2 θ (55) and r= y cosθ (56) If we substitute these into the express ...
Week 2: Continuous Charge and Gauss’s Law 71 As before with a ring, we can only easily evaluate the field on thez-axis where we ...
72 Week 2: Continuous Charge and Gauss’s Law to the sheet so that the angles from it to the edges of the sheet are close toπ/2) ...
Week 2: Continuous Charge and Gauss’s Law 73 s y x α θ dq r φ R−r R dE dE dEz Figure 13: Geometry for finding the field of a uni ...
74 Week 2: Continuous Charge and Gauss’s Law dEz dE dE α s α θ z r r sin r cos θ θ R − r cosθ y x P R dq Figure 14: Geometry for ...
Week 2: Continuous Charge and Gauss’s Law 75 The second integral is also easy enough, at least if you you remember how tointegra ...
76 Week 2: Continuous Charge and Gauss’s Law Ouch! That was a lot of work! And technically, we’re not even done – we should real ...
Week 2: Continuous Charge and Gauss’s Law 77 a θ b a a’ S’ ∆S ∆ θ n’ n a’ E Figure 15: Geometry of the flux integral over a smal ...
78 Week 2: Continuous Charge and Gauss’s Law compensate and get: ∆φ′e = |E~|cos(θ)a′b = |E~|cos(θ) ab cos(θ) = |E~|ab = ∆φe (92) ...
«
1
2
3
4
5
6
7
8
9
10
»
Free download pdf