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2. A sphere of radius R has the diclectric constant e. The net charge on the...
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....
(a) A sphere with radius R rotates with constant angular velocity . A uniform charge distribution...
(a) A sphere with radius R rotates with constant angular velocity . A uniform charge distribution is fixed on the surface. The total charge is q. Calculate the current density in this scenario where . Show how the E-field is calculated using Gauss' Law and the direction (in spherical coordinates) of the current density. We were unable to transcribe this imageWe were unable to transcribe this image7 =
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.
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the...
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. The charge within a small volume dV is dq=ρdV. The integral of ρdV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R. Hint: Let dV be a spherical shell of radius r and thickness dr. What...
3. A uniformly charged sphere of radius 'a' has a charge density po. Find D everywhere...
3. A uniformly charged sphere of radius 'a' has a charge density po. Find D everywhere using Gauss's law. Plot the magnitude of D vs R 4. A spherical shell of radius R 1 m has a surface charge density on it of пс and another spherical shell of radius R= 2m has a surface +8 Ps т? пс -6- т2 charge density of ps Find D at R= 3m
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)...
(This is based on Wangsness, Problem 10-8.) A sphere of radius a has a permanent f....
(This is based on Wangsness, Problem 10-8.) A sphere of radius a has a permanent f. (a) Find the bound charge densities in the volume and on the surface, 1. r and show that the total bound charge is zero as expected. (b) Find E everywhere, outside and inside the sphere, and verify that the normal and tangential components of E obey the expected boundary conditions at r = a. (c) Find ) everywhere, outside and inside, making sure it...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center, p(r)=(C/r2)e-kr where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q. a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q. b) Show that C=...
Charge is spread uniformly over the surface of a sphere of radius R. The potential at...
Charge is spread uniformly over the surface of a sphere of radius R. The potential at the sphere's center is V. Find an expression for the net charge Q on the sphere. Express your answer in terms of the variables R, V, and the Coulomb's constant k.
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 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...
3. A uniformly charged sphere of radius 'a' has a charge density po. Find D everywhere using Gauss's law. Plot the magnitude of D vs R 4. A spherical shell of radius R 1 m has a surface charge density on it of пс and another spherical shell of radius R= 2m has a surface +8 Ps т? пс -6- т2 charge density of ps Find D at R= 3m
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)...
(This is based on Wangsness, Problem 10-8.) A sphere of radius a has a permanent f. (a) Find the bound charge densities in the volume and on the surface, 1. r and show that the total bound charge is zero as expected. (b) Find E everywhere, outside and inside the sphere, and verify that the normal and tangential components of E obey the expected boundary conditions at r = a. (c) Find ) everywhere, outside and inside, making sure it...
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