1. The space between the spaces of a parallel plate capacitor is filled with two slabs of linear dielectric material. The slabs have different dielectric constants but the same length L, width W and thickness d. (note the area of the top (or bottom) of the capacitor is 2*L*W). Slab 1 has a dielectric constant of e1=2 and slab 2 has a dielectric constant of e2=1.5. The voltage on the top plate is Vo and the bottom plate is grounded.

a) What is the electric Field E in each slab?
b) What is the Dielectric displacement D in each slab?
c) What is the polarization P in each slab?
d) What is the magnitude of Sf, the free surface charge adjacent to each slab?
e) What is the magnitude of Sb, the bound surface charge density in each slab?
f) What is the magnitude of Vb, bound volume charge density in each slab?
g) What is the capacitance of the system and how does it compare to the capacitance of the system with no dielectrics?

See the attachment for an illustration.

2) We have an infinite electric cylinder of radius R that has a polarization

a) What is the bound volume density in the body of the cylinder
b) What is the bound surface density at r=R
c) Use Gauss' Law to find the electric field inside and outside the cylinder
d) Use a releationship between

E, D, and P to find the electric fields without using Gauss' Law.

The space between the spaces of a parallel plate capacitor is filled with two slabs of linear dielectric material. The slabs have different dielectric constants but the same length L, width W and thickness d. (note the area of the top (or bottom) of the capacitor is 2*L*W). Slab I has a dielectric constant of and slab II has a dielectric constant . The voltage on the top plate is V0 and the bottom plate is grounded.

a) What is the electric Field E in each Slab
b) What is the Dielectric displacement D in each slab
c) What is the polarization P in each slab
d) What is the magnitude of , the free surface charge adjacent to each slab
e) What is the magnitude of , the bound surface charge density in each slab
f) What is the magnitude of , bound volume charge density in each ...

Solution Summary

This solution discusses dielectrics and polarized infinite electric cylinders.

In Figure A1 in the attachment, the boundary between two ideal dielectrics is shown. Near the boundary, on Er1 side, the electric field is measured and found to be perpendicular to the boundary and equal to 100 V/m.
a) What is the direction of the electric field E, near that boundary and on Er2 side?
b) What is the magnitu

See attached file for clarity.
The electric field outside a uniformly charged, infinite cylindrical conductor is the same as if the cylinder's charge were concentrated in a thin wire along the cylinders axis. Moreover, the potential inside a uniformly charged infinite cylindrical pipe like that inside a spherical shell is co

a. A piece of plexiglass (k = 3.2) is placed above an infinite plane of charge with charge density sigma = 0.1 uC/m^2. Compute the bound charge on the bottom surface of the dielectric. Be careful of the sign.
b. A material is charged such that the electric field just inside it is 10N/C and is pointed into the boundary. The e

Consider a square plate whose sides have length l=20 cm with a total charge of +5.0 nC spread uniformly on its surface. What are the magnitude and direction of the electric field at a point 1.0 mm away from the plate's center?

A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length lambda.
Calculate the magnitude of th

An electron is released from rest 2.0 cm from an infinite charged plane. It accelerates toward the plane and collides with a speed of 1.0 x 10^7 m/s
A) What is the surface charge density of the plane in C/m^2?
B) What is the time required for the electron to travel the 2.0 cm?

See attachment for complete question and diagram.
For points far from the ends of the cylinders, determine the electric field at the following radial distances from the central axis.
(a) r = 2.0 cm
(b) r = 6.0 cm
(c) r = 13 cm

A uniform infinite line charge is parallel to the z axis and intersects the xy plane at the point (a,b,0). Find the rectangular components of E produced at the point (0,c,0). See attachment for further details to the question.

See attached file for proper format.
Find the potential Φ of the electric field at large
distance r from two close parallel infinite straight
line charges λ [C/m] and −λ [C/m] separated by
distance a << r.
Give a physical interpretation of the result.