A rectangular parallelepiped with dimensions a, b, c is filled with a dielectric in which the...
A rectangular parallelepiped with dimensions a, b, c is filled with a dielectric in which the polarization is given by kr, where k is a constant with the appropriate units, and r is the position vector of a point in the dielectric with respect to the center of the parallelepiped (i.e., the center of the parallelepiped is at the origin, and the faces are parallel to the Cartesian axes). Find the bound surface and volume charge densities in the dielectric, and show that the total bound charge is zero.
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A rectangular parallelepiped with dimensions a, b, c is filled
with a dielectric in which the...
3. [2 points] A rectangular parallelepiped with dimensions a, b, c is filled with a dielectric...
3. [2 points] A rectangular parallelepiped with dimensions a, b, c is filled with a dielectric in which the polarization is given by kr, where k is a constant with the appropriate units, and r is the position vector of a point in the dielectric with respect to the center of the parallelepiped (i.e., the center of the parallelepiped is at the origin, and the faces are parallel to the Cartesian axes). Calculate the bound surface charge density on the...
A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with...
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...
33 3 The axis of an infinitely long circular dielectric tube of inner radius ri and...
33
3 The axis of an infinitely long circular dielectric tube of inner radius ri and outer radius r. coincides with the z-axis. A polarization vector P=î3x +ģ4y exits in the dielectric with €= 2.0€. (a) Express P in cylindrical coordinate. (b) Determine the surface and volume charge densities (Ps and on (c) Show that the total bound charge is zero. (d) Find Ē and D inside the dielectric.
2. A sphere of radius R has the dielectric constant e. The net charge on the...
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....
Please answer the question on this image regarding a parallel-plate capacitor that is half-filled with 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,...
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.
The space between a parallel plate capacitor of area "A," is filled with a dielectric whose...
The space between a parallel plate capacitor of area "A," is filled with a dielectric whose permittivity varies linearly from e1 at one plate (y 0) to s2 at the other plate ( y=d). The plates have equal and opposite charge densities of magnitude o Write the equation for the permittivity as a function of position, i.e. s(y)= ? 3. AV Show the potential difference between the plates is 4. In Ae2-1 1 Determine the capacitance of the parallel plate...
Problem 3 A spherical shell of dielectric material with inner radius a and outer radius b...
Problem 3 A spherical shell of dielectric material with inner radius a and outer radius b has a polarisation P(r) kr which is frozen into the material, and where k is a constant. As usual, r is the distance from the centre. There is no free charge 1) Calculate all the bound charges 2) Calculate the electric field inside the dielectric by first calculating the electric displacement D 3) Cross-check your result by using Gauss's law (i.e. for E without...
Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a...
Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a permanent polarization set in it of P (s, φ, z-ksi where k is a constant, φ is the cylindrical azimuthal angle, and s is the usual cylindrical radius and s is the cylindrical radial unit vector. Neglect the ends of the rod, it can be considered to be infinite. a) Calculate the bound charges ơb and A-(the bound charge on the surface and in...
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...
3. [2 points] A rectangular parallelepiped with dimensions a, b, c is filled with a dielectric in which the polarization is given by kr, where k is a constant with the appropriate units, and r is the position vector of a point in the dielectric with respect to the center of the parallelepiped (i.e., the center of the parallelepiped is at the origin, and the faces are parallel to the Cartesian axes). Calculate the bound surface charge density on the...
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...
33
3 The axis of an infinitely long circular dielectric tube of inner radius ri and outer radius r. coincides with the z-axis. A polarization vector P=î3x +ģ4y exits in the dielectric with €= 2.0€. (a) Express P in cylindrical coordinate. (b) Determine the surface and volume charge densities (Ps and on (c) Show that the total bound charge is zero. (d) Find Ē and D inside the dielectric.
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....
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,...
The space between a parallel plate capacitor of area "A," is filled with a dielectric whose permittivity varies linearly from e1 at one plate (y 0) to s2 at the other plate ( y=d). The plates have equal and opposite charge densities of magnitude o Write the equation for the permittivity as a function of position, i.e. s(y)= ? 3. AV Show the potential difference between the plates is 4. In Ae2-1 1 Determine the capacitance of the parallel plate...
Problem 3 A spherical shell of dielectric material with inner radius a and outer radius b has a polarisation P(r) kr which is frozen into the material, and where k is a constant. As usual, r is the distance from the centre. There is no free charge 1) Calculate all the bound charges 2) Calculate the electric field inside the dielectric by first calculating the electric displacement D 3) Cross-check your result by using Gauss's law (i.e. for E without...
Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a permanent polarization set in it of P (s, φ, z-ksi where k is a constant, φ is the cylindrical azimuthal angle, and s is the usual cylindrical radius and s is the cylindrical radial unit vector. Neglect the ends of the rod, it can be considered to be infinite. a) Calculate the bound charges ơb and A-(the bound charge on the surface and in...
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