Conductors and Insulators, Conductors as Shields Challenge Problem Solutions

Transcription

1 Conutos n Insultos Conutos s Shiels Chllenge Polem Solutions Polem : Pt of the l this week involves shieling. We hve visuliztion to help you ette unestn this. Open it up: ieling.htm n ply with it fo while. You n move the hge oun the outsie of the shiel (o even insie) using the pmetes ius p n ngle p. You n hnge whih fiel you e looking t the totl fiel just the fiel of the extenl hge ( Fee hge ) o just the fiel of the inue hge (on the shiel). You n visulize it with gss sees o isply equipotentil steks y liking Eleti Potentil. Below e thee ptue imges. I ve lnke out the ente so tht you n t see wht is going on insie the onuto. Fo eh esie whee the hge is (ROUGH ngle n istne) tell whethe I m looking t fiel lines (gss sees) o equipotentil steks ( Eleti Potentil ) n inite whethe I m oing so fo the totl fiel o just the extenl o inue fiel. Also iefly explin HOW you know this (not just I looke oun until I ws le to epet the ptten ). Polem Solutions: () () () () These e eleti fiels lines (gss sees) of the entie fiel. We n tell euse they ome in pepeniul to the equipotentil sufe of the onuto whih is only tue fo the totl fiel (not the iniviul pts). The hge is lely elow the onuto (θ 7º) n just off the seen (R.5). () Hee the lines e neithe pepeniul no pllel to the onuto so it n t e fo the entie fiel. They loop oun looking like ipole so they e ssoite with the inue hges not the extenl hge. Ae they fiel lines o equipotentils though? Without seeing the ente this is non-tivil. If the hge wee elow the

2 fiel lines woul look vey muh like this. But sine the left n ight loes e not symmeti it must e equipotentils ete y hge on the left (R 6 θ 8º). () This one is esie. The lines wp oun the onuto so they e lely equipotentil lines ssoite with the entie fiel. The hge is on the ight (R θº)

3 Polem : Consie two neste spheil onuting shells. The fist hs inne ius n oute ius. The seon hs inne ius n oute ius. In the following fou situtions etemine the totl hge on eh of the fes of the onuting sphees (inne n oute fo eh) s well s the eleti fiel n potentil eveywhee in spe (s funtion of istne fom the ente of the spheil shells). In ll ses the shells egin unhge n hge is then instntly intoue somewhee. () Both shells e floting tht is thei net hge will emin fixe. A positive hge is intoue into the ente of the inne spheil shell. Tke the zeo of potentil to e t infinity. () The inne shell is floting ut the oute shell is goune tht is it is fixe t V n hs whteve hge is neessy on it to mintin this potentil. A negtive hge is intoue into the ente of the inne spheil shell. () The inne shell is goune ut the oute shell is floting. A positive hge is intoue into the ente of the inne spheil shell. () Finlly the oute shell is goune n the inne shell is floting. This time the positive hge is intoue into the egion in etween the two shells. In this se the questions Wht is E()/V()? e not well efine in some egions of spe. In the egions whee these questions n e nswee nswe them. In the egions whee they n t e nswee explin why n give s muh infomtion out the potentil s possile (is it positive o negtive fo exmple). Polem Solutions: ()Thee is no eleti fiel insie onuto. Also the net hge on n isolte onuto is zeo (i.e. ). Using the Guss s lw

4 > E ) ( Sine E V ) ( ) ( > V ) ( ()Sine the oute shell is now goune to mintin ) ( E outsie the oute shell. We hve. () E >

5 > V() ()Sine the inne shell is goune n to mintin E ( ) outsie the inne shell. Sine thee is no eleti fiel on the oute shell. > E( ) > V ( ) ()The eleti fiel within the vity is zeo. If thee is ny fiel line tht egn n ene on the inne wll the integl E s ove the lose loop tht inlues the fiel line woul not e zeo. This is impossile sine the eletostti fiel is onsevtive n theefoe the eleti fiel must e zeo insie the vity. The hge etween the two onutos pulls minus hges to the ne sie on the inne onuting shell n epels plus hges to the f sie of tht shell. Howeve the net hge on the oute sufe of the inne shell ( ) must e zeo sine it ws initilly unhge (floting). Sine the oute shell is goune to mintin E ( ) outsie the oute shell. Thus n E ( ) o > Fo E () is in ft well efine ut it is vey omplite. The file lines e shown in the figue elow.

6 Wht n we sy out the eleti potentil? V ( ) fo > n V( ) onstnt fo ut the potentil is vey omplite efine etween the two shells.

7 Polem 3: A onuting wie is tthe to n initilly hge spheil onuting shell of ius. The othe en of the wie is tthe to the oute sufe of neutl onuting spheil shell of ius tht is lote vey lge istne wy (t infinity). When eletostti equiliium is ehe the hge on the shell of ius is equl to ) one fouth the hge on the shell of ius. ) hlf the hge on the shell of ius. ) twie the hge on the shell of ius. ) fou time the hge on the shell of ius. e) None of the ove.

8 Polem 3 Solution:. When eletostti equiliium is ehe the two shells fom one onuting sufe n hene the potentil on tht sufe is onstnt. Beuse the two shells e vey f pt the potentil of eh shell with espet to infinity n e lulte septe. Beuse the eleti fiel outsie eh hge shell is ientil to the eleti fiel of point-like ojet with the sme hge lote t the ente of the shell. The potentil on eh shell with espet to infinity is just /. The potentil iffeene etween the two shells is zeo o / / o. Theefoe the hge on the shell of ius is equl to twie the hge on the shell of ius.

9 MIT OpenCouseWe 8.SC Physis II: Eletiity n Mgnetism Fll Fo infomtion out iting these mteils o ou Tems of Use visit: