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A spherical capacrtor consists of a spherical conducting shell of radius b and - Q that is concentric with a Smaller conducting sphere of radius a charge and charge + Q. Shorw thet er its capacitance is C= ab KeCb-a) B) Shonw that as b approaches infinity, the capacitance approaches the value a potential difference is propotional to the charge Q on the iapacitor Ke AV A First find the E- feid of the ioner sehere:

A spherical capacrtor consists of a spherical conducting shell of radius b and - Q that is concentric with a Smaller conducting sphere of radius a charge and charge + Q. Shorw thet er its capacitance is C= ab KeCb-a) B) Shonw that as b approaches infinity, the capacitance approaches the value a potential difference is propotional to the charge Q on the iapacitor Ke AV A First find the E- feid of the ioner sehere:

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Good evening! I am curious if I am just supposed to take the limit of what I got in part a) as b approaches infinity to solve for part b. Am I overthinking this? Is there an easier way or am I on the right path with my assumption? Thank you!!!!
II F9 CHAPTER 20 (36) A spherical capacrtor consists of a spherical conducting shell of radius b and charge Q and charge + Q. A) Show that ien its capacitance is delete Q that is concentric with a smaller conducting sphere of radius a C = ab Ke(b-a) enter B) Shorv that as b approaches infinity, the capacitance approaches the value a Ke return potential difference is propotional to the charge Q on the capacitor shift control C= Q AV KANDT First, find the E-field of the inner sphere: ent. -uSE THE RELATION SHP THAT E= v E•r(ifGis constant) E,= ke Q (distene It is NoT in this case so we can use dv= Edr where dvis potential change between the inner and outer sphere. KeQ are constants traveled) ROL AV = YeS dv= -S ke Q dr V= Sav= -SEdr a. -keafr"dr = -ke Q/ The 6) is becauuse as the radius ineveazes, the poten tial decreases. (AS E gets bigger, V gets snaller) use a and b as bound s, use bigger (b) as bottom bound to get a'+V since the Vrill bet when we Move from a farther get closer. Ke Q - ke Q_ Ke Q ca) 6 (b) a TUAL b (a) bkeQ-keaQ KeQ(b-a) place and ab ab put thisinto (= Q (=Q C= & ab Ke&(6-a) TkeCb-a) =C Ke Q(b-a) ab %3D ab
Transcribed Image Text:II F9 CHAPTER 20 (36) A spherical capacrtor consists of a spherical conducting shell of radius b and charge Q and charge + Q. A) Show that ien its capacitance is delete Q that is concentric with a smaller conducting sphere of radius a C = ab Ke(b-a) enter B) Shorv that as b approaches infinity, the capacitance approaches the value a Ke return potential difference is propotional to the charge Q on the capacitor shift control C= Q AV KANDT First, find the E-field of the inner sphere: ent. -uSE THE RELATION SHP THAT E= v E•r(ifGis constant) E,= ke Q (distene It is NoT in this case so we can use dv= Edr where dvis potential change between the inner and outer sphere. KeQ are constants traveled) ROL AV = YeS dv= -S ke Q dr V= Sav= -SEdr a. -keafr"dr = -ke Q/ The 6) is becauuse as the radius ineveazes, the poten tial decreases. (AS E gets bigger, V gets snaller) use a and b as bound s, use bigger (b) as bottom bound to get a'+V since the Vrill bet when we Move from a farther get closer. Ke Q - ke Q_ Ke Q ca) 6 (b) a TUAL b (a) bkeQ-keaQ KeQ(b-a) place and ab ab put thisinto (= Q (=Q C= & ab Ke&(6-a) TkeCb-a) =C Ke Q(b-a) ab %3D ab
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