Using Dirac delta functions in the appropriate coordinate system, express the following charge distributions as three dimensional charge densities ρ(r). One way to check your answer is to integrate your ρ(r) over all space and see that you get the correct total charge. a) In spherical coordinates, a charge Q uniformly distributed over an infinitesmally thin spherical shell of radius R. b) In cylindrical coordinates, a charge λ per unit length uniformly distributed over an infinitely long cylindrical surface of radius b. c) In cylindrical coordinates, a charge Q spread uniformly over a flat circular disk of negligible thickness and radius R, centered in the xy plane at z=0. d) The same as (c), but using spherical coordinates.
Using Dirac delta functions in the appropriate coordinate system, express the following charge distributions as three dimensional charge densities ρ(r). One way to check your answer is to integrate your ρ(r) over all space and see that you get the correct total charge.
a) In spherical coordinates, a charge Q uniformly distributed over an infinitesmally thin spherical shell of radius R.
b) In cylindrical coordinates, a charge λ per unit length uniformly distributed over an infinitely long cylindrical surface of radius b.
c) In cylindrical coordinates, a charge Q spread uniformly over a flat circular disk of negligible thickness and radius R, centered in the xy plane at z=0.
d) The same as (c), but using spherical coordinates.
Trending now
This is a popular solution!
Step by step
Solved in 10 steps with 9 images
