Dimensions of rectangular parallelepiped is a*b*c.
So the distance between the origin and top or bottom surface is c/2.
Here
So the surface charge density on both the surface is given by
This is the surface charge density on both top and bottom surface each.
3. [2 points] A rectangular parallelepiped with dimensions a, b, c is filled with a dielectric...
Please answer the question on this image regarding a parallel-plate capacitor that is half-filled with dielectric Problem 4 (6 points) A parallel-plate capacitor is half-filled with a slab of material of dielectric constant e, as shown in the figure. d/2 a) By what factor is the capacitance increased as a result of the presence of the dielectric? b) If the top and bottom conducting plates of the capacitor have surface charge density to and –o, respectively, identify the location, sign,...
4. Consider the dielectric slab shown below: The electric field within the slab is: E(T) = 2 âz [V/m] and the susceptibility of the dielectric is 2.0, find: (a) the permittivity and relative permittivity of the dielectric. (b) the electric flux density within the slab. (c) the polarization vector within the slab. (d) the volume bound charge density within the slab. (e) the surface bound charge density at the top and bottom of the slab.
Problem 5 The space between the plates of a parallel-plate capacitor, shown below, is filled with two slabs of different dielectric materials. The slab at the top has thickness 2d and a relative dielectric constant of er1 = 3 and the one at the bottom has thickness d and a relative dielectric constant of er2 = 2. The capacitor plates have surface area S. a. Assume a total charge of +Q on the top plate and -Q on the bottom plate. Find...
A spherical shell linear dielectric of e inner radius a and outer radius for b is filled with is embedded with a free charge density of ρ(r) = kr. (a) Find the electric displacement D in each slab. (b) Find the electric field E in each slab. (c) Find the polarization P in each slab (d) Find the potential difference between the plates (e) Find the location and amount of all bound charge.
2. A sphere of radius R has the dielectric constant e. The net charge on the sphere is zero but it has the polarization kr (C/m2) in spherical coordinates (k is a constant with the appropriate units). a) (12 points) Calculate the bound charge density pb (C/m3) and the surface bound charge density ơb (C/m2). b) (15 points) Calculate the E-field for rR and for r>R. Use Coulomb's law with the net bound charge density (volume and surface) as needed....
A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a "frozen-in" polarization P(r) 0 r<a P(r) ksin(0)/r r a<r<b where k is a constant, r is the distance from the center, and r is the radial unit vector. There is no free charge in the problem 1. Find expressions for all the bound (volume and surface) charge. Interpret with a diagram. 2. Determine the total bound charge. Be aware if the bound charge...
3. Two dielectric materials (material 1 and 2) are combined either in series (Case A) or parallel (Case B) arrangements as shown in the figure below. The relative permittivity for material one is 10 while the relative permittivity for material two is 3000. A voltage of 100 volts is applied across the entire the top surface while the bottom is grounded (0 Volts) in both cases. The z- direction is up with z-0 representing the bottom ground. Calculate for each...
(1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two laye ers of dielectrics, di and de thick, with permittivities s and s2, respectively. Ignoring the ringe effect at the four edges (assuming rectangular plates), find the fields Ei and E2 in the t dielectric ctrics if a voltage V(assumed positive) is applied to the top plate with regard to the bottom plate. (Note: both magnitudes and directions needed.) (2) Find the...
Problem 1. Electrostatics (1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two layers of dielectrics, ch and d2 thick, with permittivities fringe effect at the four edges (assuming rectangular plates), find the fields Ei and Es in the two dielectrics if a voltage V (assumed positive) is applied to the top plate with regard to the bottom plate. (Note: both magnitudes and directions needed.) and a, respectively. Ignoring the (2) Find...
2 3 4 ds Electric Field 2. Just like in question 1, a charged particle with charge qs 20 nC is placed at the origin. This is the "source particle". The charge on the source particle creates an electric field at every point in space around the particle. a. Use your answer in question la and the equation FE to determine the electric field vector (E) at position 1. Draw the electric field vector with its tail at position 1....