![4. Consider the dielectric slab shown below: The electric field within the slab is: E(T) = 2 âz [V/m] and the susceptibility](http://img.homeworklib.com/questions/1d969bb0-3a86-11eb-bbd4-b3a4878d58fa.png?x-oss-process=image/resize,w_560)
Homework Answers
![12.655x 3x8 85xia ECO) = 2 Es år um ê within slab) x=2 a) Era H x = 1+2=[3] Ez&& = 36 = 348-858101 -[3.655x10.flm) b) D= EE =](http://img.homeworklib.com/questions/1e6909d0-3a86-11eb-89c4-6165e954981b.png?x-oss-process=image/resize,w_560)
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4. Consider the dielectric slab shown below: The electric field within the slab is: E(T) =...
The space between the plates of a parallel-plate capacitor, shown below, is filled with two slabs of different dielectric materials
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 dielectric slab is placed in a external field as shown. Outside the slab, the electric...
A dielectric slab is placed in a external field as shown. Outside the slab, the electric field isEs=(10.ON/C)x. Inside the slab, the electric field isEs= (3.5N/C)x. What is the dielectric constant? 0.35 O 1.0 O 1.5 2.0 2.9 QUESTION 20 For the previous question what is the charge density of the left side of the slab? -1.1x10-11 C/m2 0 -3.1x10-11 C/m2 -8.9x10-11 C/m2 -5.8x10-11 C/m2 0 -1.2x10-11 C/m2
5. (20 points) For many dielectric materials, the relationship between the displacement field D a...
5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is...
(a) For a linear dielectric, the polarization P can be written in terms of the electric...
(a) For a linear dielectric, the polarization P can be written in terms of the electric field E as P = EoXE. Using this, show that the electric displacement can be written as D= EE where e is the permittivity. (b) Consider the interface between two dielectric materials, which has a free surface charge of. (bi) Using Gauss's law for materials, show that Dabove – Debelow = of where Dabove and Dbelow are the perpendicular (to the interface) components of...
3. Two dielectric materials (material 1 and 2) are combined either in series (Case A) or parallel (Case B) arrangements...
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...
A homogeneous dielectric sphere, of radius a and relative permittivity Er, is situated in air. There...
A homogeneous dielectric sphere, of radius a and relative permittivity Er, is situated in air. There is a free volume charge density ρ(r)-Po r/a (0 a) throughout the sphere volume, where r is the distance from the sphere center (spherical radial coordinate) and po is a constant. (a) Determine the electric displacement vector D for 0 r 〈 00, (b) what is the electric field inside the sphere (0 r a)? (c) What is the electric field outside the sphere...
Please step by step for D(electric flux density), E(electric field), V(electric potantial), P(polarization vector) ? A...
Please step by step for
D(electric flux density), E(electric field), V(electric potantial),
P(polarization vector) ?
A positive point charge Q is at the center of a spherical dielectric shell of an inner radius Ri and an outer radius RO. Determine E, V, D, and P as functions of the radial distance R. a)R>RO b)Ri<R<RO c)R<R find it. E1 = 60 €2 = Erzo (E3 = 6,360 = 0 - R + Ro conductive dielectric dielectric
20 volts are applied to a parallel-plate capacitor with a distance of 1 mm separating two...
20 volts are applied to a parallel-plate capacitor with a distance of 1 mm separating two electrodes and with a dielectric material having e_r= 120. The surface area of each plate is 1cm^2 and e_0= 8.85 x 10^-12 Fm^-1. Please calculate (1 F = 1 C/V): (a) the total charge density (b) the bound charge density (c) the polarization (d) the permittivity of the dielectric (e) the electric displacement (f) electric susceptibility (g) the capacitance
14. (15 points) Consider a cylindrical waveguide shown in Fig. 2.3 (a) (7 points) Electric field ...
14. (15 points) Consider a cylindrical waveguide shown in Fig. 2.3 (a) (7 points) Electric field inside a cylindrical waveguide filled with a dielectric with relative permittivity e, is given by the following expression: o ex ar Inb/a r (b) (7 points) Calculate corresponding magnetic field H (c) (3 points) Calculate the Poyinting vector S and the power flowing through the surface a <r<b, z = h dl fig 2,3 20 2 2
14. (15 points) Consider a cylindrical waveguide...
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 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.
A dielectric slab is placed in a external field as shown. Outside the slab, the electric field isEs=(10.ON/C)x. Inside the slab, the electric field isEs= (3.5N/C)x. What is the dielectric constant? 0.35 O 1.0 O 1.5 2.0 2.9 QUESTION 20 For the previous question what is the charge density of the left side of the slab? -1.1x10-11 C/m2 0 -3.1x10-11 C/m2 -8.9x10-11 C/m2 -5.8x10-11 C/m2 0 -1.2x10-11 C/m2
5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is...
(a) For a linear dielectric, the polarization P can be written in terms of the electric field E as P = EoXE. Using this, show that the electric displacement can be written as D= EE where e is the permittivity. (b) Consider the interface between two dielectric materials, which has a free surface charge of. (bi) Using Gauss's law for materials, show that Dabove – Debelow = of where Dabove and Dbelow are the perpendicular (to the interface) components of...
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...
A homogeneous dielectric sphere, of radius a and relative permittivity Er, is situated in air. There is a free volume charge density ρ(r)-Po r/a (0 a) throughout the sphere volume, where r is the distance from the sphere center (spherical radial coordinate) and po is a constant. (a) Determine the electric displacement vector D for 0 r 〈 00, (b) what is the electric field inside the sphere (0 r a)? (c) What is the electric field outside the sphere...
Please step by step for
D(electric flux density), E(electric field), V(electric potantial),
P(polarization vector) ?
A positive point charge Q is at the center of a spherical dielectric shell of an inner radius Ri and an outer radius RO. Determine E, V, D, and P as functions of the radial distance R. a)R>RO b)Ri<R<RO c)R<R find it. E1 = 60 €2 = Erzo (E3 = 6,360 = 0 - R + Ro conductive dielectric dielectric
14. (15 points) Consider a cylindrical waveguide shown in Fig. 2.3 (a) (7 points) Electric field inside a cylindrical waveguide filled with a dielectric with relative permittivity e, is given by the following expression: o ex ar Inb/a r (b) (7 points) Calculate corresponding magnetic field H (c) (3 points) Calculate the Poyinting vector S and the power flowing through the surface a <r<b, z = h dl fig 2,3 20 2 2
14. (15 points) Consider a cylindrical waveguide...
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