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A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/R) for r≤R ρ(r)=0for r≥R where ρ0=3Q/πR3 is a positive constant. Electric field for this charge distribution is  E(r)= kQ/r2 for r≥R kQ/r2 [4(r3/R3) − 3(r4/R4)] for r≤R   a) Show that for r≥R the potential is identical to that produced by a point charge Q. (Take the potential to be zero at infinity.) b) Obtain an expression for the electric potential valid in the region r≤R

A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/R) for r≤R ρ(r)=0for r≥R where ρ0=3Q/πR3 is a positive constant. Electric field for this charge distribution is  E(r)= kQ/r2 for r≥R kQ/r2 [4(r3/R3) − 3(r4/R4)] for r≤R   a) Show that for r≥R the potential is identical to that produced by a point charge Q. (Take the potential to be zero at infinity.) b) Obtain an expression for the electric potential valid in the region r≤R

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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A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/R) for r≤R

ρ(r)=0for r≥R

where ρ0=3Q/πR3 is a positive constant. Electric field for this charge distribution is 

E(r)= kQ/r2 for r≥R

kQ/r2 [4(r3/R3) − 3(r4/R4)] for r≤R

 

a) Show that for r≥R the potential is identical to that produced by a point charge Q. (Take the potential to be zero at infinity.)

b) Obtain an expression for the electric potential valid in the region r≤R.

8 of 8 Review Constants Show that for r> R the potential is identical to that produced by a point charge Q. (Take the potential to be zero at infinity.) A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: p(r)= po (1-r/R) p(r) 0 Po = 3Q/TR is a positive constant. Electric field for this charge distribution is Essay answers are llmited to about 500 words (3800 characters maximum, Including spaces). for r <R for r 2 R where 3800 Character(s) remaining %3D kQ/r² for r 2 R E(+) = { ke [4 -3 for r< R 4- 3 for r <R Submit Request Answer Part B Obtain an expression for e electric potential valid in the region r R. Express your answer in terms of the given quantities and appropriate constants. ΑΣΦ
Transcribed Image Text:8 of 8 Review Constants Show that for r> R the potential is identical to that produced by a point charge Q. (Take the potential to be zero at infinity.) A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: p(r)= po (1-r/R) p(r) 0 Po = 3Q/TR is a positive constant. Electric field for this charge distribution is Essay answers are llmited to about 500 words (3800 characters maximum, Including spaces). for r <R for r 2 R where 3800 Character(s) remaining %3D kQ/r² for r 2 R E(+) = { ke [4 -3 for r< R 4- 3 for r <R Submit Request Answer Part B Obtain an expression for e electric potential valid in the region r R. Express your answer in terms of the given quantities and appropriate constants. ΑΣΦ
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