b) What is the volume charge density of an electric dipole consisting of a point charge-q at the origin and a point charge +q at a(bar)

c) What is the charge density of a uniform infinitesimally thin spherical shell shell of Radius R and total charge Q which is centered at the origin.
note: the integral over all space must equal Q)

Solution Summary

PDF and Word document attached show how to give an expression for charge density at a point and other questions.

We have a long coaxial cable with an inner solid wire of radius a and outer
metal shell of radius b. On the inner wire, thevolumechargedensity is given by ks2 .
On the outer shell, the linear chargedensity (along the axis) is given by λ.
(a) Draw a picture that illustrates this arrangement.
(b) What is the lin

a. dielectric sphere of radius R is polarized so that P=(k/r)r1, r1 being the unit radial vector.
c. Calculate the potential inside/outside the sphere
d. Sketch a curve of potential versus distance from r=0 to r=infinity.

Please show all work and show all equations used and diagrams, etc. etc. so I understand completely please.
1) Charge is placed on the surface of a 2.7cm radius isolated conducting sphere. The surface densitycharge is uniform and has the value 6.9*10^-6C/m^2. The total charge on the sphere is:
2) A spherical shell has a

Given two plane-parallel electrodes, space d, at voltages 0 and V_0, find the current density if an unlimited supply of electrons at rest is supplied to the lower potential electrode. Neglect collisions.

(a) Write an expressionforthe electric chargedensity p (r) of a point charge q at r/. Make
sure that thevolume integral of p equals q.
(b) What is thechargedensity of an electric dipole, consisting of a point charge -q at the
origin and a point charge +q at a?
(c) What is thechargedensity of a uniform, infini

We have a spherical volume with R=1m. Inside a uniform chargedensity increases with a constant rate of 2 C/(m^3s). The increase is related to a uniform chargedensity that enters radially through the surface. Use the continuity equation to calculate the current density through the surface. See attached

A quarter spherical volume has a chargedensity f(x,y,z) = 3 sqrt(x^2+y^2+z^2) mico coulombs per cubic meter. Calculate the total charge by evaluating the triple integral (please see the attached file). Do so by changing the spherical coordinates. Don't forget to calculate the Jacobian.
** Please see the attached file for th

4a. Consider the parallel plate capacitor, where the surface chargedensity is 0.02 uC/m^2, and the distance between the plate is 0.01m. What is the potential difference between the two plates?
4b. What would be the change in potential energy of the electron as it moves from the negative plate to the positive plate?
4c.

(See attached file for full problem description)
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1. Consider two infinite parallel plane conducting plates, of finite thickness, with separation d. Suppose a chargedensity of sigma; is placed on one plate, while the other plate has -2sigma.
A) Determine the resulting charge densities on each of the 4 surfaces
B) De