You Comments I feel like I watch a pe-lectue, and agee with eveything said, but feel like it doesn't click until lectue. Conductos and Insulatos with Gauss's law please...so basically eveything! I don't think we go ove enough actual poblems duing lectue that will help with ou homewok. Hi pofesso. I am eally soy fo my extemely unstudious physics pelectue attitude duing this pelectue. You see, today is my bithday and I spent it calling home and enjoying the simple joys of life... a little too simple to compehend physics pelectues today, though physics is a joy. xplain how the -field at a point an abitay distance fom an infinite plane of chage can be constant. It doesn't make intuitive sense. I guessed on most of the checkpoints... Does that mean that physics is just not fo me? Can you explain induced chages on conductos moe thooughly? Can you ty to incopoate moe moden/inteesting physics topics into you lectues? ven if it's just a quick blip at the stat of the lectue, it would be nice to think about how what we'e leaning now applies to moe advanced physics and/o engineeing applications. Why do we talk about infinitely long planes and cylindes? Ae we using it as a stepping stone to moe eal-wold situations o ae thee actually cases in which thee is something like an infinitely long chaged cylinde? lecticity & Magnetism Lectue 4, Slide
lecticity & Magnetism Lectue 4 Today s Concepts: A) Conductos B) Using Gauss Law lectomagnetism is so easy! (Said no one eve...) lecticity & Magnetism Lectue 4, Slide
Conductos and Insulatos Conductos chages fee to move e.g. metals Insulatos chages fixed e.g. glass 6 Physics Lectue 4, Slide 3
Define: Conductos Chages Fee to Move Claim: inside any conducto at equilibium Chages in conducto move to make field zeo inside. (Induced chage distibution). If, then chage feels foce and moves! Claim: xcess chage on conducto only on suface at equilibium Why? Apply Gauss Law Take Gaussian suface to be just inside conducto suface eveywhee inside conducto da Gauss Law: suface da Q enc o Q enc suface SIMULATION 9 lecticity & Magnetism Lectue 4, Slide 4
Gauss Law Conductos Induced Chages suface da Q enc o ALWAYS TRU! If choose a Gaussian suface that is entiely in metal, then so Q enclosed must also be zeo! Q enc A o How Does This Wok? Chages in conducto move to sufaces to make Q enclosed. We say chage is induced on the sufaces of conductos lecticity & Magnetism Lectue 4, Slide 5
Chage in Cavity of Conducto A paticle with chage -Q is placed in the cente of an unchaged conducting hollow sphee. How much chage will be induced on the inne and oute sufaces of the sphee? Q oute A) inne -Q, oute Q B) inne -Q/, oute Q/ C) inne, oute D) inne Q/, oute -Q/ ) inne Q, oute -Q Q inne -Q Gauss Law: suface Since in conducto Qenc da o Q enc 3 lecticity & Magnetism Lectue 4, Slide 6
Infinite Cylindes A long thin wie has a unifom positive chage density of.5 C/m. Concentic with the wie is a long thick conducting cylinde, with inne adius 3 cm, and oute adius 5 cm. The conducting cylinde has a net linea chage density of -4C/m. What is the linea chage density of the induced chage on the inne suface the conducting cylinde (l i ) and on the oute suface (l o )? l i :.5 C/m -4 C/m -.5 C/m -.5 C/m of l o l o : -6.5 C/m -4 C/m.5 C/m -.5 C/m A B C D l i 6 lecticity & Magnetism Lectue 4, Slide 7
Gauss Law I'm confused with how to detemine which gaussian suface is best suited to calculate an electic field da Q enc ALWAYS TRU! In cases with symmety can pull outside and get Qenc A In Geneal, integal to calculate flux is difficult. and not useful! To use Gauss Law to calculate, need to choose suface caefully! ) Want to be constant and equal to value at location of inteest OR ) Want dot A so doesn t add to integal 7 lecticity & Magnetism Lectue 4, Slide 8
Gauss Law Symmeties Q ALWAYS TRU! da enc In cases with symmety can pull outside and get Qenc A Spheical Cylindical Plana A 4 Q enc 4 A L l A lecticity & Magnetism Lectue 4, Slide 9
CheckPoint D) The field cannot be calculated using Gauss Law ) None of the above TH CUB HAS NO GLOBAL SYMMTRY! TH FILD AT TH FAC OF TH CUB IS NOT PRPNDICULAR OR PARALLL 3D POINT SPHRICAL D LIN CYLINDRICAL D PLAN PLANAR lecticity & Magnetism Lectue 4, Slide
CheckPoint 3. What is diection of field between blue and ed sphees? A) Outwad B) Inwad C) Zeo The electic lines oigin fom q and teminate at q negative chage is pulled towads positive chage No electic field within a conducto Caeful: what does inside mean? This is always tue fo a solid conducto (within the mateial of the conducto) Hee we have a chage inside 5 lecticity & Magnetism Lectue 4, Slide
CheckPoint 3.3 What is diection of field OUTSID the ed sphee? A) Outwad B) Inwad C) Zeo 7 lecticity & Magnetism Lectue 4, Slide
CheckPoint What is magnitude of at dashed line ()? A) Plug into the Gauss' Law equation B) Zeo Thee is no chage enclosed in the sphee of adius 3 ( b - 3 a ) 3 C) (4pi^)p(pi)(4/3)(b^3-a^3)/e and the pi*4 cancels. D) None of above 3 lecticity & Magnetism Lectue 4, Slide 3
CheckPoint 4 In which case is at point P the biggest? A) A B) B C) the same Thee is an oveall ight field in Case A, in Case B the negative and positive planes cancel out. The sum of the fields is geate in case B. The negative is close than the ightmost positive so it has a geate effect. Chaged infinite planes ceate constant electic fields. In Case A, thee is one positive field, and in Case B thee ae two positive and one negative. In Case B, one negative and one positive cancel out, leaving only one positive electic field. lecticity & Magnetism Lectue 4, Slide 4
Supeposition: Lets do calculation! P P Case A - Case B 4 lecticity & Magnetism Lectue 4, Slide 5
3Q y neutal conducto x Calculation Can we please go ove the conducting sphee with the conducting shell aound it? Point chage 3Q at cente of neutal conducting shell of inne adius and oute adius. a) What is eveywhee? Fist question: Do we have enough symmety to use Gauss Law to detemine? Yes, Spheical Symmety (what does this mean???) Magnitude of depends only on R A) B) C) Diection of is along Diection of is along Diection of is along xˆ ŷ ˆ D) None of the above 4 lecticity & Magnetism Lectue 4, Slide 6
3Q y neutal conducto x Calculation Point chage 3Q at cente of neutal conducting shell of inne adius and oute adius. A) What is eveywhee? We know: magnitude of is fcn of diection of is along We can use Gauss Law to detemine Use Gaussian suface sphee centeed on oigin da Q enc ˆ < 45 da 4 Q enc 3 4 Q 3Q A) B) C) < < 3Q 4 3Q 4 A) B) C) > 3Q 4 4 3Q ( - ) lecticity & Magnetism Lectue 4, Slide 7
3Q y neutal conducto x Calculation Point chage 3Q at cente of neutal conducting shell of inne adius and oute adius. A) What is eveywhee? We know: < > 3Q 4 B) What is chage distibution at? A) B) C) da < > Q enc < < 3Q Gauss Law: Similaly: 3Q 4-3Q Qenc 4 48 lecticity & Magnetism Lectue 4, Slide 8
3Q y neutal conducto < x Calculation Suppose give conducto a chage of -Q A) What is eveywhee? B) What ae chage distibutions at and? da > Q enc 3Q -3Q Q A) B) 4 4 3Q Q A) B) 4 4 3Q Q < < C) 4 Q C) 4 Q 5 lecticity & Magnetism Lectue 4, Slide 9