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.
Due to dielectric material, bound charges will be there, but bound charges will be 0 for r>b as total bound charges are always 0(volume bound charges are equal and opposite in sign to surface bound charges).
Effect of bound charges will be there in displacement density
for a Comment regarding any queries....
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.
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 has an inner radius of a and an outer radius of b. The shell is made of a dielectric material and has a polarization P f. The shell is neutral and there is no free charge. Determine the electric field in the three regions: (i) r < a; (i) a <r< b; and (ii) r > b using two different methods. (a) Determine the bound charges in each region and use Gauss' law to determine the electric...
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.
Consider a spherical shell with inner radius a and outer radius b. A charge density σ A cos(9) is glued over the outer surface of the shell, while the potential at the inner surface of the shell is V (8) Vo cos(0). Find electric potential inside the spherical shell, a<r<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....
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 thick spherical dielectric shell (inner radius a, outer radius b) has a "frozen-in" polarization: where k is a constant. Find the electric field for: a) r< a, b) a < r <b, andc) r > b
The figure below shows a spherical shell with uniform volume charge density ρ = 2.00 nC/m3, inner radius a = 5.0 cm, and outer radius b = 2.60a.What is the magnitude of the electric field at the following radial distances:(a) r = 0:(b) r = a/2.00:(c) r = a:(d) r = 1.50a:(e) r = b:(f) r = 3.00b:
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...
A charged spherical insulator shell has inner radius a and outer radius b. The charge density on the shell is p. What is the electric field inside the shell? Zero a. (1/4TTeo) 9/12 Ob. pleo C. P(b3 - 23)/(3e0r2) Od. P(r3 - 23)/(3e0r2) e.