A non-uniform but spherically symmetric distribution of charge has a charge density given as follows: ρ = ρo ( 1 – r/R ) for r ≤ R ρ = 0 for r > R where ρo = 3Q/πR3 is a constant. a) Show that the total charge contained in the charge distribution is Q. b) Using Gauss’ Law, obtain an expression for the electric field in the region r ≥ R. c) Using Gauss’ Law, obtain an expression for the electric field in the region r ≤ R.
A non-uniform but spherically symmetric distribution of charge has a charge density given as follows: ρ = ρo ( 1 – r/R ) for r ≤ R ρ = 0 for r > R where ρo = 3Q/πR3 is a constant. a) Show that the total charge contained in the charge distribution is Q. b) Using Gauss’ Law, obtain an expression for the electric field in the region r ≥ R. c) Using Gauss’ Law, obtain an expression for the electric field in the region r ≤ R.
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A non-uniform but spherically symmetric distribution of charge has a charge density given as follows:
ρ = ρo ( 1 – r/R ) for r ≤ R
ρ = 0 for r > R
where ρo = 3Q/πR3 is a constant.
- a) Show that the total charge contained in the charge distribution is Q.
- b) Using Gauss’ Law, obtain an expression for the electric field in the region r ≥ R.
- c) Using Gauss’ Law, obtain an expression for the electric field in the region r ≤ R.
- d) Compare your results in (b) and (c) for r = R.
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