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Make a plot of V versus r and E versus r and note any similarities and/or Are there locations where E = 0 but V is nonzero? Explain. dv Using E -VV = = - verify that you can get back the expression for E from dr dv -VV - verify that you can get back the expression for E from dr C. differences. d. the result of part a. e. the result of part b. Using E =

Make a plot of V versus r and E versus r and note any similarities and/or Are there locations where E = 0 but V is nonzero? Explain. dv Using E -VV = = - verify that you can get back the expression for E from dr dv -VV - verify that you can get back the expression for E from dr C. differences. d. the result of part a. e. the result of part b. Using E =

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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Suppose you have a solid sphere of total charge Q and radius R with uniform charge density p. Let r represent distances from the center of the sphere. a. Using AV = V(rf) – V(r;) = - = ri – SĒ · dr determine the electric potential as a function of distance r from the center of the sphere for points outside the sphere r > R. Be sure to draw a diagram and label any quantities of interest. (Hint: Remember that V = 0 at r = ∞o so you will want to integrate from r₁ = ∞o torf = r. See page 716 of the text if you are having trouble.) b. Repeat this calculation for points inside the sphere r ≤ R. Be sure to draw a diagram and label any quantities of interest. (Hint: You need to integrate from r; = ∞ to rƒ = r, but remember that E has different values inside and outside the sphere.) C. Make a plot of V versus r and E versus r and note any similarities and/or differences. Are there locations where E = 0 but V is nonzero? Explain. dv d. Using Ē= -√V = ✩ verify that you can get back the expression for È from dr the result of part a. dv e. Using Ē = -VV ✩ verify that you can get back the expression for E from dr the result of part b. =
Transcribed Image Text:Suppose you have a solid sphere of total charge Q and radius R with uniform charge density p. Let r represent distances from the center of the sphere. a. Using AV = V(rf) – V(r;) = - = ri – SĒ · dr determine the electric potential as a function of distance r from the center of the sphere for points outside the sphere r > R. Be sure to draw a diagram and label any quantities of interest. (Hint: Remember that V = 0 at r = ∞o so you will want to integrate from r₁ = ∞o torf = r. See page 716 of the text if you are having trouble.) b. Repeat this calculation for points inside the sphere r ≤ R. Be sure to draw a diagram and label any quantities of interest. (Hint: You need to integrate from r; = ∞ to rƒ = r, but remember that E has different values inside and outside the sphere.) C. Make a plot of V versus r and E versus r and note any similarities and/or differences. Are there locations where E = 0 but V is nonzero? Explain. dv d. Using Ē= -√V = ✩ verify that you can get back the expression for È from dr the result of part a. dv e. Using Ē = -VV ✩ verify that you can get back the expression for E from dr the result of part b. =
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