E field of a uniform and planar distribution of charge
A uniform surface charge density of 5nC/m2 is present in the
region x=0, -2<y<2 and all z. if ε=ε0, find E at:
a) PA(3,0,0)
b) PB(0,3,0).
A planar slab of thickness of 5.00 cm has a uniform
volume charge density of 7.20×10-2 C/
m3. Find the magnitude of the electric field at
all points in space both inside and outside the slab, in terms of
x, the distance measured from the central plane of the slab. What
is the field for x = 1.25 cm?
What is the field for x = 10.00 cm?
A
spherical shell of radius a has a uniform surface charge density σ
and rotates with a constant angular velocity ω in relation to an
axis that passes through its center. In this situation, determine
the magnetic dipole moment μ of the spherical shell.
Consider a spherical charge distribution of radius R with a
uniform charge density ρ.
Using Gauss' Law find the electric field at distance r from the
axis where r < R.
A metal sphere of radius a has a uniform (free) charge
density σf on its surface. The permittivity of the
dielectric region surrounding the sphere varies as , where
r is the radial coordinate.
(1 pts) Determine the polarization P and electric field
intensity E inside the sphere.
(3 pts) Determine the polarization P and electric field
intensity E in the dielectric.
(5 pts) Calculate all bound charge densities, ρb and
σb. Is the dielectric homogeneous?
(1 pts) Test whether...
An infinitely long hollow cylinder of radius R is carrying a
uniform surface charge density σ (φ).
(a) Determine the general form of the solution of Laplace’s
equation for this geometry.
(b) Use the boundary condition σ(φ) = σ0cos(φ) to determine
the potential inside and outside of the cylinder.
(c) Using your answer to part (b), determine the electric
field inside and outside of the cylinder.
A nonconducting disk has a radius R, carries a uniform surface
charge density s, and rotates with angular speed w.
(a) Consider an annular strip that has radius ?, width ??, and
charge ??. Show that the
current produced by this strip is ?? = ?????.
(b) Show that the net magnetic field at the center of the disk
is ?)???⁄2.
(c) Find the magnetic field on the axis of the disk, a distance
z from the center.
Derive expressions for the surface current density and
surface charge density, for the TE10 and TE11 modes of a
rectangular waveguide.
The old answers on Chegg are either wrong or
incomplete, please dont copy them.
2. A thin disk of radius R and uniform surface charge density
sigma rotates about its axis of symmetry with angular velocity
omega = omega zhat.
(a) What is the current density K(s) where s is the distance
from the center?
(b) Find B at the center of the disk (z=0, s=0) using
Bio-Savart's law. (It's a simple integral).
(c) What is the magnetic dipole moment of the disk?
Two charged droplets of toner ink behave as two shells of
uniform surface charge density. (Toner is an insulating material,
not conductive.) The two drops have total charge qi, radiusRi, and
centre positionri,i= 1,2. Assuming the drops do not overlap, derive
the electric potential, V(r), everywhere inside and outside the
spheres. Is the voltage (potential) inside shell 1 constant?