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3 The axis of an infinitely long circular dielectric tube of inner radius ri and...
A dielectric sphere of radius a has a ”frozen in” polarization given by P (r) = krrˆ in standard ...
A dielectric sphere of radius a has a ”frozen in” polarization
given by P (r) = krrˆ in standard spherical coordinates, with the
origin of the coordinate system at the center of the sphere. (A)
The sphere is surrounded by a conducting shell of inner radius a
and outer radius b > a. The total charge on the conducting shell
is zero. Is there an induced charge on the inner and outer surfaces
of the conducting shell? If so, what...
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...
Electrostatics problem 2. An infinitely long circular cylinder of radius a and dielectric constant E is...
Electrostatics problem
2. An infinitely long circular cylinder of radius a and dielectric constant E is placed with its axis along the z-axis and is put in an electric field which would have been uniform in the absence of the cylinder, pointing along the x-axis (see figure). Find the total electric field at all points outside and inside the cylinder. Find the bound surface charge density.
2. Given a spherical dielectric shell (inner radius a, outer radius b, dielectric constant K) and...
2. Given a spherical dielectric shell (inner radius a, outer radius b, dielectric constant K) and a point charge Q, which is infinitely separated from the shell. Now let Q be placed at the center of the shell. Determine the change in the energy of the system (Hint: the induced charge densities σα and ơb due to the centered Q on the inner and outer surfaces are-(Q/4 a 2)(K-1)/K] and +(Q/4 b2)(K-1)/ki, respectively.)
2. Given a spherical dielectric shell (inner...
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...
An infinitely long insulting cylindrical shell has inner radius R1 and outer radius R2 and a...
An infinitely long insulting cylindrical shell has inner radius R1 and outer radius R2 and a uniform volume charge density p. Determine E for r<R1 and for R1<r<R2 and for r>R2
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) = k (r+ P(E)=(-+) 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....
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded...
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius Rs (called the shield) as shown in Figure 8. The conductors carry equal and opposite currents, I, distributed uniformly across their cross sections. Determine the magnetic field at a distance r from the axis for: (a) r< Ri (b) Ri < R2 Page 2 (c) R2<r<Rs (d) R3 (e) Plot the magnitude...
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...
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 sphere of radius a has a ”frozen in” polarization
given by P (r) = krrˆ in standard spherical coordinates, with the
origin of the coordinate system at the center of the sphere. (A)
The sphere is surrounded by a conducting shell of inner radius a
and outer radius b > a. The total charge on the conducting shell
is zero. Is there an induced charge on the inner and outer surfaces
of the conducting shell? If so, what...
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...
Electrostatics problem
2. An infinitely long circular cylinder of radius a and dielectric constant E is placed with its axis along the z-axis and is put in an electric field which would have been uniform in the absence of the cylinder, pointing along the x-axis (see figure). Find the total electric field at all points outside and inside the cylinder. Find the bound surface charge density.
2. Given a spherical dielectric shell (inner radius a, outer radius b, dielectric constant K) and a point charge Q, which is infinitely separated from the shell. Now let Q be placed at the center of the shell. Determine the change in the energy of the system (Hint: the induced charge densities σα and ơb due to the centered Q on the inner and outer surfaces are-(Q/4 a 2)(K-1)/K] and +(Q/4 b2)(K-1)/ki, respectively.)
2. Given a spherical dielectric shell (inner...
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...
An infinitely long insulting cylindrical shell has inner radius R1 and outer radius R2 and a uniform volume charge density p. Determine E for r<R1 and for R1<r<R2 and for r>R2
Problem 3 A spherical shell of dielectric material with inner radius a and outer radius b has a polarisation, P(r) = k (r+ P(E)=(-+) 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....
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius Rs (called the shield) as shown in Figure 8. The conductors carry equal and opposite currents, I, distributed uniformly across their cross sections. Determine the magnetic field at a distance r from the axis for: (a) r< Ri (b) Ri < R2 Page 2 (c) R2<r<Rs (d) R3 (e) Plot the magnitude...
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...
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