Question

Make a side by side comparison for the solutions of example 3.9 (the potential inside and outside a sphere with charge density ? = ? cos ? glued on its surface) and example 4.2 (the potential inside and outside a uniformly polarized sphere). Compare them according to:

a) The given information

b) The equation to be solved (Poisson’s or Laplace’s)c) The
boundary conditions

d) Applying the boundary conditions

e) Final solution

Example 3.9. A specified charge density u0(0) is glued over the surface of a spherical shell of radius R. Find the resulting potential inside and outside the sphere.

Example 4.2 Find the electric field produced by a uniformly polarized sphere of radius R.

Answer #1

A surface charge density sigma(theta)=[sigma_o(cos(theta))] is
glued to the surface of a spherical shell of radius R. There is a
vacuum with no charges both inside and outside of the shell.
Calculate the electrostatic potential and electric field both
inside and outside of the spherical shell.
Side note: sigma_o is sigma subscript o.

A surface charge density sigma(theta)=[sigma_o(cos(theta))] is
glued to the surface of a spherical shell of radius R. There is a
vacuum with no charges both inside and outside of the shell.
Calculate the electrostatic potential and the electric field both
inside and outside the spherical shell. (the "_" is a subscript in
sigma_o).

A solid, nonconducting sphere of radius R = 6.0cm is charged
uniformly with an electrical charge of q = 12µC. it is enclosed by
a thin conducting concentric spherical shell of inner radius R, the
net charge on the shell is zero.
a) find the magnitude of the electrical field
E1 inside the sphere (r < R) at the
distance r1 = 3.0 cm from the center.
b) find the magnitude of the electric field E2
outside the shell at the...

A thin, uniformly charged spherical shell has a potential of 727
V on its surface. Outside the sphere, at a radial distance of 20.0
cm from this surface, the potential is 403 V.
(1) Calculate the radius of the sphere.
(2) Determine the total charge on the sphere
(3) What is the electric potential inside the sphere at a radius
of 3.0 cm
(4) Calculate the magnitude of the electric field at the surface
of the sphere.
(5) If an...

The potential at the surface of a sphere (radius R) is given by
Vo=Kcos3D, Where D is theta,K is a constant. Find the potential
inside and outside the sphere, as well as the surface charge
density s(D) on the sphere.(Assume there is no charge inside or
outside the sphere).

26. A spherical shell of radius R carries a surface charge σ =
σ0 Sin[θ]. Find the potential inside and outside the
sphere, calculating the coefficients explicitly up to A6
and B6.

Consider a solid uniformly charged copper sphere with charge Q
and radius R. Showing all Steps,
(a) Calculate the potential of the spherical charge inside and
outside of the sphere.
(b) Calculate the electric field of the spherical charge from
the potential in part (a) for the inside and outside regions.

A charge is spread out uniformly over a small non-conducting
sphere. The small sphere shares a center with a larger spherical
shell with an inner radius of 6 ?? and an outer radius of 12 ??. a)
Using Gauss’ Law, what is the magnitude of the charge on the
nonconducting sphere if the field from the sphere is measured to be
8200 ?/? when 0.5 ?? from the center? b) What is the surface charge
density on the inside of...

A plastic sphere with a radius of 4 cm is surrounded by a
concentric metal shell of 7 cm inside radius, and 10 cm outside
radius. The outer shell has a net charge of +5 Coulombs, while the
plastic sphere inside has a uniformly distributed charge of -10
Coulombs.
What is the electric potential relative to infinity at a
distance 15 [cm] from the center of the plastic sphere i.e. outside
the conducting shell, and why?
2b. What net charge...

Consider two concentric spherical shells with different radii,
namely one is inside the other. The spherical shell inside has
radius R1 = 7.00 cm and charge q1 = +3.00×10^-6 C; the spherical
shell outside has radius R2 = 17.0 cm and charge q2 = −5.00×10^-6
C. For both shells charges are distributed uniformly over their
surfaces. Assume that V = 0 at large distances from both
shells.
A) Find the electric potential of the two shells at the distance r...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 11 minutes ago

asked 14 minutes ago

asked 18 minutes ago

asked 19 minutes ago

asked 39 minutes ago

asked 56 minutes ago

asked 56 minutes ago

asked 56 minutes ago

asked 1 hour ago