Electricity & Magnetism Lecture 22. Electricity & Magne/sm Lecture 22, Slide 1
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1 Electicity & Magnetism Lectue 22 Electicity & Magne/sm Lectue 22, Slide 1
2 You Comments You LIED about electic poten/al being the hadest pat of the couse! Please go though eveything in detail because this is a confusing pelectue and I don't undestand most of it at all. I feel like I don't undestand this well enough to even ask ques/ons about it. LiEle bit shell- shocked ight now. THAT WAS AWESOME!! DISCUSS ALL PLEASE!!!! ALL TRUE We will ty to make clea, at least the BIG IDEAS wave equa/ons, this is my fist /me seeing them (aside fom oscillatos) Text B field looks like the shadow of E field, o the othe way aound Do we have to know how to solve diffeen/al equa/ons o will the poblems be limited to these specific types of examples? We will discuss waves You will not have to solve new diff eqns Moe concened about the midtem. Electicity & Magne/sm Lectue 22, Slide 2
3
4 Ode online.
5 What We Knew Befoe Pelectue 22 Electicity & Magne/sm Lectue 22, Slide 3
6 Afte Pelectue 21: Modify Ampee s Law Electicity & Magne/sm Lectue 22, Slide 4
7 Displacement Cuent Real Cuent: Chage Q passes though aea A in /me t: Displacement Cuent: Electic flux though aea A changes in /me Fee space Electicity & Magne/sm Lectue 22, Slide 5
8 Calculation Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. At /me t 1, what is the magne/c field B 1 at a adius (point d) in between the plates of the capacito? d I 1 R Q 1 Conceptual and Stategic Analysis Chage Q 1 ceates electic field between the plates of C Chage Q 1 changing in /me gives ise to a changing electic flux between the plates Changing electic flux gives ise to a displacement cuent I D in between the plates Apply (modified) Ampee s law using I D to detemine B Electicity & Magne/sm Lectue 22, Slide 6
9 Calculation Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. c d I 1 R Compae the magnitudes of the B fields at points c and d. Q 1 A) B c < B d B) B c = B d C) B c > B d What is the diffeence? Apply (modified) Ampee s Law R point c: I(enclosed) = I 1 X point d: I D (enclosed) < I 1 Electicity & Magne/sm Lectue 22, Slide 7
10 Calculation Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. d E R What is the magnitude of the electic field between the plates? A) B) C) D) I 1 Q 1 Q 1 R Electicity & Magne/sm Lectue 22, Slide 8
11 Calculation Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. d E R What is the electic flux though a cicle of adius in between the plates? A) B) C) D) I 1 Q 1 R E = ~E ~A Electicity & Magne/sm Lectue 22, Slide 9
12 Calculation Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. d I 1 E R What is the displacement cuent enclosed by cicle of adius? A) B) C) D) Q 1 R Electicity & Magne/sm Lectue 22, Slide 10
13 Calculation Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. hat is the magnitude of the B field at adius? I 1 Q 1 d E R I B d = µ 0 (I + I D ) A) B) C) D) I Ampee s Law: R B d = µ 0 (I + I D ) B(2 ) = µ I 1 2 R 2! Electicity & Magne/sm Lectue 22, Slide 11
14 Calculate Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. hat is the magnitude of the B field at adius? I 1 Q 1 d E R I B d = µ 0 (I + I D ) R Let: I1 = 1 A R = 1 m What is B at = 0.5 m? (answe on next page) Electicity & Magne/sm Lectue 22, Slide 11
15 B = 1 x 10 7 T answe
16 CheckPoint B is popo/onal to I but At A, B = 0!! Electicity & Magne/sm Lectue 22, Slide 13
17 CheckPoint 4 A B C Fom the calcula/on we just did: Electicity & Magne/sm Lectue 22, Slide 12
18 Follow-Up Switch S has been open a long /me when at t = 0, it is closed. Capacito C has cicula plates of adius R. At /me t = t 1, a cuent I 1 flows in the cicuit and the capacito caies chage Q 1. What is the /me dependence of the magne/c field B at a adius between the plates of the capacito? (A) (B) (C) B at fixed is popo/onal to the cuent I Close switch: V C = 0 I = V/R a (maximum) I exponen/ally decays with /me constant τ = R a C Electicity & Magne/sm Lectue 22, Slide 14
19 Follow-Up 2 Suppose you wee able to chage a capacito with constant cuent (does not change in /me). Does a B field exist in between the plates of the capacito? A) YES B) NO Constant cuent Q inceases linealy with /me Theefoe E inceases linealy with /me, E = Q/(Aε 0 ) de/dt is not zeo Displacement cuent is not zeo B is not zeo! Electicity & Magne/sm Lectue 22, Slide 15
20 We leaned about waves in Physics 140
21 How can light move at the same velocity in any ine/al fame of efeence? That's eally tippy. see PHYS 285 Electicity & Magne/sm Lectue 22, Slide 17
22 Electicity & Magne/sm Lectue 22, Slide 18
23 Electicity & Magne/sm Lectue 22, Slide 19
24 CheckPoint 6 E x = E 0 sin(kz ωt) E = E 0 sin (kz ωt): E depends only on z coodinate fo constant t. z coodinate is same fo A, B, C Electicity & Magne/sm Lectue 22, Slide 20
25 CheckPoint 7 E x = E 0 sin(kz ωt) E = E 0 sin (kz ωt): E depends only on z coodinate fo constant t. z coodinate is same fo A, B, C Electicity & Magne/sm Lectue 22, Slide 21
26 Clicke Question E x = E 0 sin(kz ωt) Conside a point (x,y,z) at /me t when E x is nega/ve and has its maximum value. At (x,y,z) at /me t, what is B y? A) B y is posi/ve and has its maximum value B) B y is nega/ve and has its maximum value C) B y is zeo D) We do not have enough infoma/on Electicity & Magne/sm Lectue 22, Slide 22
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