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
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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.
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
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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.
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