Question

• A sphere of radis s as a constant volume charge density > 0 • A puin partide - and cro < inlevala with the electric potential AV() shown below. The particle has che or via la le right all willa velocity AV (Volts) I=0 1. (15 points) What is the eletric field inside und eutside of the chute distribution. To s you need to show WIT rulli fra exi 1. (7 points) Craph the cleetric field (r) function of the distanee for 205 S2 2. ( points) You assemble a concentric spherical conducting shell of inner radius and outer radius cas shown, the conducting material is electrically noutro audio electroetatic equilibrium Plot Llle agnitude of clue clectric field is a function or for Dar2.. 2. 17 points) For - = -10,w= 1 kg, V-1 V, and region I fort > D? Explain. = 2 /, will the particle be found in conductor 3. (10 points) Graph the electric potential energy, kinetic energy, and total energy in the same plot for 20 20 4. (1 points) Craph the mwition of the particle in function of time, manly partico) (2 points) Suppoee you need a 15F Capacitor, but the stockroom has only 20 XF and 50 MF capacitors How can the desired capacitance be achieved under these circumstancesDraw your circuit 3. (5 points) If any, what is the chanc/roen charge density pala, on the shell? 4. (2 points in the process of constructing the sholl did you doposit energy into the system? extract is? O meile? Explai..

Answer 1

volume = to charge density radues = a a Gaussian surface at a Jet us consider distance is from centre Now Eids - Oene where Oene = charge enclosed & Eas caso = cene co É and ñ are along rodeal direction) co - - E gds = cene EF - Cene - 0 82 un to

Now denu = Sede where de a small volume clement = 82 sind do do do Ηθι γκα 27 Acne = to 82 Sino do do do 0 DO a ene = fox 4 1 " sino do do . 41 - An to 3 382 from 0 Ecocad = I REO - tor untora - for (for unside)

Now for s a Dere = lede (P= to guien) SSS to 87 sono do do dd ( some do = 20 = to AT baz do 2 ap= 25 - Po 47 a ( here we took limit on 8 from to a from 0 because charge only exist in this region Ecosal = 1 Cene 2- Чn to = 1 4REO to un a² 82 3 = to a 38082 380 :: Electric field, Ē Crea) = for å & Electric field, Elora - 360 82 - where a= roduis