chp26_explained

# chp26_explained - Week 4 Chapter 26 Problem 15 Two...

This preview shows pages 1–3. Sign up to view the full content.

Week 4, Chapter 26 Problem 15 Two conducting spheres of radius a are separated by a distance l>>a; since the distance is large, neither sphere appects the other’s electric field significantly, and the fields remain spherically symmetric. (a) If the spheres carry equal but opposite charges ±q, show that the potential difference between them is 2kq/a. (b) Write an expression for the work dW involved in moving an infinitesimal charge dq from the negative to the positive sphere. (c) Integrate your expression to find the work involved in transferring a charge Q from one sphere to the other, assuming both are initially uncharged.. (a) Since the electric fields of each sphere are not affected substantially by each other’s presence, their voltage will not be either, so we can use the standard formula for the potential of a sphere or point charge with r = infinity as the reference point. The potential of each conducting sphere is going to be equal to the point charge potential at a the radius a. The potential will not increase higher than that because the electric field inside the conductor is zero, so the potential cannot increase once inside that radius a. a kq V a V a V V a kq a V a kq a V 2 ) ( ) ( ) ( , ) ( 2 1 2 1 = ! " = ! " = = (b) If we move a differential amount of charge onto the sphere, it will not change the voltage, so taking the differential of W=qV, we’ll get dW=Vdq. dq a kq dW Vdq dW 2 = = (c) If both spheres are initially uncharged, then the lower bound of our integration is 0, and since we’re charging them up to a voltage Q, that’s our upper bound. Notice that while the potential doesn’t really change much for any little dq added, it does charge over the course of the integration, starting with V = 0 and ending with V = 2kQ/a. ( ) a kQ W Q a k W q a k W dq a kq W Q Q 2 2 0 2 0 0 2 2 2 = ! = " = = #

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 36 A capacitor consists of a conducting shell of radius b. Show that its capacitance is ( ) a b k b a C !
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern