You Comments Do we still get the 8% back on homewok? It doesn't seem to be showing that. Also, this is eally stating to make sense to me! I am a little confused about the diffeences in solid conductos, solid insulatos, and instances whee thee is a combination of both and we need to find the electic field. I had some difficulty undestanding the mateial, especially the significance of chage density and the induced chages on a conducting sphee. Thee wee a few times duing the pe lectue whee they said "The electic field hee MUST be " and I didn't undestand why How do you know what Gaussian suface to use to calculate the electic field poduced by a paticula object? Like if you'e calculating the electic field poduced a distance fom solid spheical conducto you would use a concentic sphee as the Gaussian suface. Then fo instance fo a cube, would you use a concentic cube? Sometimes I get confused as to what adius to plug in fo volumes and aeas. Could we go ove when to use the adius of the chage and when to use the adius of the Gaussian suface? lecticity & Magnetism Lectue 4, Slide 1
lecticity & Magnetism Lectue 4 Today s Concepts: A) Conductos B) Using Gauss Law lecticity & Magnetism Lectue 4, Slide
Conductos and Insulatos Conductos chages fee to move e.g. metals Insulatos chages fixed e.g. glass 6 Physics 1 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 11 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 13 Gauss Law: suface da Since in conducto Q o enc o Q enc -Q Q inne Since conducto is unchaged Q inne Q oute Qoute -Q inne 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 -1.5 C/m A B C D l i 16 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! 1) Want to be constant and equal to value at location of inteest OR ) Want dot A so doesn t add to integal 17 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 1 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 1D PLAN PLANAR lecticity & Magnetism Lectue 4, Slide 1
CheckPoint 3.1 What is diection of field between blue and ed sphees? A) Outwad B) Inwad C) Zeo 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 The field points fom the positive chage to the negative chage. It must point inwad to cancel out the field outwad due to the chage inside the shell to completely cancel out the e-field inside the shell The fields cancel out. 5 lecticity & Magnetism Lectue 4, Slide 11
CheckPoint 3.3 What is diection of field OUTSID the ed sphee? A) Outwad B) Inwad C) Zeo 7 lecticity & Magnetism Lectue 4, Slide 1
CheckPoint What is magnitude of at dashed line ()? A) It is p/e because that is the e-field due to the outside of the sphee and the inside must be equal to that in magnitude. B) Zeo Within <a thee is no chage enclosed. C) 3 3 ( b - a ) units wok out. 3 D) None of above its something that is 1/. 3 lecticity & Magnetism Lectue 4, Slide 13
CheckPoint 4 In which case is at point P the biggest? A) A B) B C) the same The electic field in case B is zeo, and the electic field in case A is nonzeo. The fist positive and negatively chaged planes in case B both have fields pointing to the ight. These ae the stongest fields because they'e closest to the point P. The ightmost positive field will point to the left, but this will be weake than eithe of the two fields pointing to the ight, giving an oveall geate field magnitude in case B. If you supeposition the electic fields, they cancel out in case B so the electic field is the same in both cases. 3 lecticity & Magnetism Lectue 4, Slide 14
Supeposition: Lets do calculation! P P Case A - Case B 4 lecticity & Magnetism Lectue 4, Slide 15
y Calculation 3Q neutal conducto 1 x Point chage 3Q at cente of neutal conducting shell of inne adius 1 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 17
3Q y neutal conducto 1 x Calculation Point chage 3Q at cente of neutal conducting shell of inne adius 1 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 < 1 45 da 4 Q enc Q 3 1 4 3Q A) B) C) 1 < < 1 3Q 4 1 3Q 4 1 A) B) C) > 1 3Q 4 1 3Q 4 ( - ) lecticity & Magnetism Lectue 4, Slide 18
3Q y neutal conducto 1 x Calculation Point chage 3Q at cente of neutal conducting shell of inne adius 1 and oute adius. A) What is eveywhee? We know: < 1 > 1 3Q 4 B) What is chage distibution at 1? A) B) C) da < > Q enc 1 < < 3Q 1 Gauss Law: Similaly: 3Q 4-3Q Qenc 1 4 1 48 lecticity & Magnetism Lectue 4, Slide 19
3Q y neutal conducto 1 < 1 x Calculation Suppose give conducto a chage of -Q A) What is eveywhee? B) What ae chage distibutions at 1 and? da > Q enc 3Q -3Q 1 Q A) B) 1 4 1 4 3Q Q A) B) 1 4 1 4 3Q Q 1 < < C) 1 4 Q C) 1 4 Q 5 lecticity & Magnetism Lectue 4, Slide