Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, El-gunde (Electomgnetism, 14--6, kl 9.-15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue notes. Define the nottions you e using popely. Pesent you guments in detils. Good luck! 1 Find the electicl field distnce z bove the cente of flt ing of dii nd b (Fig. 1 with sufce chge density ( / Help: You my use the following fomul of integl clcultion (Bet, p. 156, integl 114. d 1 / 1 1 1. Fig. 1. Conside cpcito fomed by two concentic sphees of dii The eltive dielectic pemittivity between the sphees vies s (, cpcitnce of the system. e the ngles in the spheicl coodintes nd b, espectively. 1 cos sin ;;. Find
Umeå Univesitet, Fysik Vitly Bychkov Two coil cylindes of dii nd b ( b, length L nd vey high conductivity e septed by modetely conductive substnce with conductivity ( /. Potentil of the oute cylinde is, the inne cylinde is gounded. Find potentil distibution between the cylindes. Find esistnce of the system. (4 p 4 An infinitely long nd wide pln lye of thickness is ( b z b distibuted s spce. b is plced pependicul to z-. The lye is mde of nonline electic mteil with polistion P P ˆ z P z / b. Find the electic field E nd the potentil eveywhee in 5 An infinitely long stight cylinde of dius j ˆ j / cylindicl coodintes nd cies cuent distibuted s, whee the cylinde is is diected long the z-is, is the ngle in is the distnce fom the is. Mgnetic pemebility is equl inside the cylinde. The only mgnetic field in the system is tht poduced by the cylinde. Find the foce d F cting on cuent element jdv of the cylinde. Hint: Think bout the diection of the mgnetic field; wht kind of cuent geomety do we hve in the poblem? (4 p
Umeå Univesitet, Fysik Vitly Bychkov Physics: Foundtions of electomgnetism (El-gunde, 14-6-1, kl 9.-15. Hjälpmedel: Students cn use ny book(s including the compendium. Mino notes in the books e lso llowed. Define you nottions popely. Pesent guments in detils. Good luck! 1 An infinitely long conducting semi-cylinde of dius is distibuted ove the sufce s cos K K cies sufce cuent, which. Find mgnetic field on the z-is. y K z Fig. 1. A cpcito is mde of two long coil metllic cylindes of dii nd b. The spce between the cylindes is filled with dielectic of eltive pemittivity chnging long the is s 1 cos ( kz / k. Find cpcitnce C pe one peiod of the dielectic stuctue. (4 p Conside distibuted chge with density whee dius s system. ( / fo nd fo, is dius in the spheicl system of coodintes. eltive pemittivity vies with fo nd 1 fo. Find electosttic enegy of the /
Umeå Univesitet, Fysik 4 Vitly Bychkov 4 A dipole is plced t distnce h fom n infinite gounded conducting plte with the dipole moment diected nomlly to the plte, see Fig.. Find the foce cting on the dipole. (4 p P z h conducto Fig.. 5 An infinitely long lye of width is plced pependicul to z-is within z. The lye cies cuent distibuted s j j ( z / ˆ. Find mgnetic field B eveywhee in spce. Hint: Think if mgnetic field on the cente-plne z is zeo o non-zeo. (4 p
Umeå Univesitet, Fysik 5 Vitly Bychkov Physics: Foundtions of electomgnetism (El-gunde, 1--7, kl 16.-. Hjälpmedel: Students my use ny book(s including the compendium. Mino notes in the books e lso llowed. Define you nottions popely. Pesent guments in detils. Good luck! 1 Conside segment of coll pln ing - shown in Fig. 1 (inne dius, oute dius b, totl ngle density. Find the electic field E, negligible thickness in z diection with unifom sufce chge in the coodinte oigin. y b Fig. 1. Conside pllel-plte cpcito mde of two conductive cicul pltes of dii septed by the distnce d of eltive pemittivity chnging with ngle s (Fig.. The spce between the pltes is filled with dielectic 1 cos. Find cpcitnce neglecting boundy effects t the sides of the cpcito. (4 p d Fig..
Umeå Univesitet, Fysik 6 Vitly Bychkov Conside thick conducting spheicl shell with inne nd oute dii espectively. Conductivity of the shell vies with dius s ( /. Potentil diffeence between the inne nd oute sufces of the shell is nd. Find enegy dissiption in the shell pe unit time. (4 p b, 4 Conside plsm (ionised gs consisting of electons (chge e nd ions (chge e. The plsm is bounded by n infinitely lge plte of potentil s shown in Fig.. Ion concenttion n i in the plsm is fied nd equl n. At the sme time potentil of the plte cuses non-unifom distibution of electons ccoding to the eltion n e n (1 e / T, whee T is constnt electon tempetue (mesued in enegy units. Find potentil distibution in plsm. (4 p n i = n n e = n (1 + e/t Fig.. 5 Conside n infinitely long cylinde of dius distibuted s j ˆ j ep( /, whee with the volume cuent density is the distnce fom the cylinde is nd is ngle ound the is (in cylindicl coodintes. Find mgnetic field B eveywhee in spce. (4 p