P.3-8 A spherical distribution of charge \(\rho=\rho_{0}\left[1-\left(R^{2} / b^{2}\right)\right]\) exists in the region \(0 \leqslant R \leqslant b\). This charge distribution is concentrically surrounded by a conducting shell with inner radius \(R_{i}(>b)\) and outer radius \(R_{o} .\) Determine \(\mathbf{E}\) everywhere.
P.3-9) Two infinitely long coaxial cylindrical surfaces, \(r=a\) and \(r=b(b>a)\), carry surface charge densities \(\rho_{s a}\) and \(\rho_{s b},\) respectively.
a) Determine \(\mathbf{E}\) everywhere.
b) What must be the relation between \(a\) and \(b\) in order that \(\mathbf{E}\) vanishes for \(r>b ?\)
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 positive point charge of magnitude 2.6 HC is at the center of an uncharged spherical conducting shell of inner radius 65 cm and outer radius 110 cm (a) Find the charge densities on the inner and outer surfaces of the shel -0.49 0.17 μC/m2 (inner) μC ', /m2 (outer) Find the total charge on each surface 2.6 2.6 HC (inner) IC (outer) (b) Find the electric field everywhere Er 65 cm 23374 E65 < r< 110 cm0 r2 Er110...
5. Total: 5 pts] A spherical conducting ball of radius a carries a net charge of Q, and it is surrounded by a concentric spherical conducting shell with zero net charge. The shell has inner radius b and outer radius c (see Fig. 1 a) 2 points] Find the total surface charge on the surfaces at r = a, r = b, and r = c. b) [3 points Find E and V as a function of radius from zero...
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...
G1. What is E for a spherical shell of charge p=0 for r < R1, p = po for R; <r < R2 and • P=0 for r > R2? R2 R1 Po What is the electric field for an infinitely long cylindrical pipe, inner radius Ry, outer radius R, and with p=Ar2 in the pipe wall between R, and R,? R2 R1 For problem G1 what is V in each region of space?
A spherical conducting shell with no net charge on it has a point charge q on its center. a.) What is the surface charge density on its inner surface (r=a), and what's the surface charge density on its outer surface (r=b)? b.) If charge Q' is added to the conducting shell, what are the new charge densities on the inner and outer surfaces? Please show all work!!!
A perfectly conducting spherical shell has an inner radius a and an outer radius b as shown below. The region r< a is hollow. The entire shell has a net charge of Q IC] on it because it has been stuck by lightning. Determine the electric field vector in all three regions: r<a, a< r b, and r > b. Determine the surface charge densities po and po on the two metal surfaces. Explain how this problem illustrates the Faraday...
Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by Es = -4.8x 103 N/C. What is the linear charge density of the shell?
P8. Suppose a neutral spherical conducting shell has an inner radius of 10.0 cm and an outer radius of 15.0 cm. A charge of +4.50 μC is placed at the center of the shell. Calculate the charge densities on the inner and outer surfaces of the shell
10.4) Thick insulating shell A thick insulating spherical shell has inner radius a and outer radius b. The shell carries a uniform volume charge density po. [A cross-sectional view of the shell is shown to the right.] (a) Consider a spherical Gaussian surface of radius r concentric with the shell. How much charge is enclosed in the Gaussian surface for p <a, a <r <b, and r > b? (b) What does symmetry dictate about the magnitude and direction of...