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(This is based on Wangsness, Problem 10-8.) A sphere of radius a has a permanent f....
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....
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)...
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)...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d)...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d) Vo cos θ. There is no a) Find the potential everywhere inside and outside the sphere. b) Find the electric field everywhere inside the sphere. (You will find it easier to convert the potential to Cartesian coordinates and then find the field.) c) Find the charge density σ(0) on the surface of the sphere using Gauss' law. charge inside or outside the sphere.
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that...
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. direction of E as a function of position within the sphere. Be sure to state the magnitude and 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that...
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. Be sure to state the magnitude and direction of E as a function of position within the sphere. 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
(16 pts total) The potential at the surface of a sphere of radius R is given...
(16 pts total) The potential at the surface of a sphere of radius R is given by Vo k(35cos 0-30cos +5cos+3) where k is a constant. Assume there is no charge inside or outside the sphere. 2. a. (5 pts) Write Vo in terms of Legendre polynomials b. (6 pts) Determine the boundary conditions and find the potential inside and outside the sphere. (5 pts) Find the surface charge density σ(θ) at the surface of the sphere. C.
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...
Select Tru or False. 1. A conducting sphere with charge Q at equilibrium has zero E...
Select Tru or False. 1. A conducting sphere with charge Q at equilibrium has zero E field inside it. The E field outside is the same as that of a point charge Q, E=keQ/r2. The potential outside it is the same as that of a point charge Q. V= keQ/r. (r is the distance to the center). The potential inside the conducting sphere is equal to the potential at its surface. V= keQ/R. (R is the radius of the sphere)...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having an electric potential of zero. A point charge Q is brought toward the sphere along the z- axis and is placed at the point ะ-8. As the point charge approaches the sphere mobile charge is drawn from the ground into the sphere. This induced charge arranges itself over the surface of the sphere, not in a uniform way, but rather in such a way...
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....
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)...
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)...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d) Vo cos θ. There is no a) Find the potential everywhere inside and outside the sphere. b) Find the electric field everywhere inside the sphere. (You will find it easier to convert the potential to Cartesian coordinates and then find the field.) c) Find the charge density σ(0) on the surface of the sphere using Gauss' law. charge inside or outside the sphere.
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. direction of E as a function of position within the sphere. Be sure to state the magnitude and 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. Be sure to state the magnitude and direction of E as a function of position within the sphere. 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
(16 pts total) The potential at the surface of a sphere of radius R is given by Vo k(35cos 0-30cos +5cos+3) where k is a constant. Assume there is no charge inside or outside the sphere. 2. a. (5 pts) Write Vo in terms of Legendre polynomials b. (6 pts) Determine the boundary conditions and find the potential inside and outside the sphere. (5 pts) Find the surface charge density σ(θ) at the surface of the sphere. C.
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...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having an electric potential of zero. A point charge Q is brought toward the sphere along the z- axis and is placed at the point ะ-8. As the point charge approaches the sphere mobile charge is drawn from the ground into the sphere. This induced charge arranges itself over the surface of the sphere, not in a uniform way, but rather in such a way...
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