A sphere of radius R carries a polarization P(r)=krsin(theta) {vector sign above p and r} where k...
Homework Answers
a)
bound charge
= - div.P
=- k sin theta + k cos theta
= k (cos theta - sin theta)
b)
total bound charge
= int (-div P)* 2pi r^2 dr sin theta d theta
= [k *2 pi r^3]/3 * [cos theta - sin theta] sin theta d theta
theta varies form 0 to pi
carry out this integration
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A sphere of radius R carries a polarization
P(r)=krsin(theta) {vector sign above p and
r}
where k...
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 sphere of radius R carries a volume charge density ρ(r) = kr, where k is...
A sphere of radius R carries a volume charge density ρ(r) = kr, where k is a constant and r is in spherical coordinates. Calculate the energy of this configuration, check the answer by calculating it in four ways.
2. A sphere of radius R has the diclectric constant e. The net charge on the...
2. A sphere of radius R has the diclectric constant e. The net charge on the sphere is zero but it has the polarization P-krf (C/n2) in spherical coordinates (k is a constant with the appropriate units) a) (12 points) Calculate the bound charge density ps(C/m3) and the surface bound charge density ơs(C/m2). b) (15 points) Calculate the E-field for R and for R. Use Coulomb's law with the net bound charge density (volume and surface) as oded. Which component(s)...
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A dielectric sphere of radius a has a polarization P Kr2f. Find the electric field and electric displacement at distance r from center, a) for r < a (inside the sphere), and b) for r>a (outside the sphere)
A spherical shell of inner radius a and outer radius b carries a polarization P = kr (rhat) (a < r < b). Calculate the bound charges sigma_b (inner and outer surfaces) and rho_b, and find the el...
A spherical shell of inner radius a and outer radius b carries a polarization P = kr (rhat) (a < r < b). Calculate the bound charges sigma_b (inner and outer surfaces) and rho_b, and find the electric field E in all three regions.
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded in the sphere is a free-charge density ρ= k/r, where k is constant and r is the distance from the sphere's center. (a) Show that ker 2REo is the electrie field inside the sphere. (b) The electric field outside the sphere is 26or2 Find the scalar potential at the center of the sphere, taking the zero of potential at infinite radial distance 2. In...
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...
A point charge q is placed in the center of a solid dielectric sphere of radius R and permittivit...
Pleasee I need the best answer!
A point charge q is placed in the center of a solid dielectric sphere of radius R and permittivity e constant. Assume that the dielectric material of the sphere is linear and that the point charge in the center of the sphere is the only free charge a Determine the electrical displacement inside and outside the sphere. b. Determine the electric field inside and outside the sphere c. Determine the polarization vector using (1)...
Long dielectric cylinder of radius R carries a built-in electrostatic polarization P that is linearly proportional...
Long dielectric cylinder of radius R carries a built-in electrostatic polarization P that is linearly proportional to the distance to the axis, P-ar, P is directed along the radius-vector r. Cylinder is being rotated around the axis with angular velocity c. Find the magnetic field B on axis.
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...
2. A sphere of radius R has the diclectric constant e. The net charge on the sphere is zero but it has the polarization P-krf (C/n2) in spherical coordinates (k is a constant with the appropriate units) a) (12 points) Calculate the bound charge density ps(C/m3) and the surface bound charge density ơs(C/m2). b) (15 points) Calculate the E-field for R and for R. Use Coulomb's law with the net bound charge density (volume and surface) as oded. Which component(s)...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
A dielectric sphere of radius a has a polarization P Kr2f. Find the electric field and electric displacement at distance r from center, a) for r < a (inside the sphere), and b) for r>a (outside the sphere)
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded in the sphere is a free-charge density ρ= k/r, where k is constant and r is the distance from the sphere's center. (a) Show that ker 2REo is the electrie field inside the sphere. (b) The electric field outside the sphere is 26or2 Find the scalar potential at the center of the sphere, taking the zero of potential at infinite radial distance 2. In...
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...
Pleasee I need the best answer!
A point charge q is placed in the center of a solid dielectric sphere of radius R and permittivity e constant. Assume that the dielectric material of the sphere is linear and that the point charge in the center of the sphere is the only free charge a Determine the electrical displacement inside and outside the sphere. b. Determine the electric field inside and outside the sphere c. Determine the polarization vector using (1)...
Long dielectric cylinder of radius R carries a built-in electrostatic polarization P that is linearly proportional to the distance to the axis, P-ar, P is directed along the radius-vector r. Cylinder is being rotated around the axis with angular velocity c. Find the magnetic field B on axis.
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