(a) Find the electric field intensity on the z axis produced by a cone surface that carries charge density ρs(r) = ρ0 /r
Posted: Tue Apr 12, 2022 10:08 am
(a) Find the electric field intensity on the z axis produced by
a cone surface
that carries charge density ρs(r) = ρ0 /r C/m2 in free space. The
cone has its
vertex at the origin and occupies the region θ = α, 0 < r <
a, and 0 < ϕ <
2π in spherical coordinates. Differential area for a cone is given
in spherical
coordinates as da = r sin α dr dϕ. (b) Find the total charge on the
cone. (c)
Specialize your result of part a to the case in which α = 90°, at
which the
cone flattens to a disk in the xy plane. Compare this result to the
answer
to problem 2.23. (d) Show that your part a result becomes a point
charge
field when z >> a. (e) Show that your part a result becomes
an inverse-zdependent
E field when z << a.
a cone surface
that carries charge density ρs(r) = ρ0 /r C/m2 in free space. The
cone has its
vertex at the origin and occupies the region θ = α, 0 < r <
a, and 0 < ϕ <
2π in spherical coordinates. Differential area for a cone is given
in spherical
coordinates as da = r sin α dr dϕ. (b) Find the total charge on the
cone. (c)
Specialize your result of part a to the case in which α = 90°, at
which the
cone flattens to a disk in the xy plane. Compare this result to the
answer
to problem 2.23. (d) Show that your part a result becomes a point
charge
field when z >> a. (e) Show that your part a result becomes
an inverse-zdependent
E field when z << a.