Consider a nonconducting sphere and a concentric nonconducting spherical shell, shown in the figure. The inner sphere has non uniform charge density ρ1 = ρ0 / r, where ρ0 is a constant, in units of C/m2 and radius a. The outer spherical shell has uniform charge density ρ2 , inner radius b, and outer radius c. Find the magnitude of the electric field for a < r < b, in terms of the given variables, as needed.

Consider a nonconducting sphere and a concentric nonconducting spherical shell, shown in the figure. The inner sphere has non uniform charge density ρ1 = ρ0 / r, where ρ0 is a constant, in units of C/m2 and radius a. The outer spherical shell has uniform charge density ρ2 , inner radius b, and outer radius c. Find the magnitude of the electric field for a < r < b, in terms of the given variables, as needed.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 43P

See similar textbooks

Similar questions

An insulating solid sphere of radius a has a uniform volume charge density and carries a total positive charge Q. A spherical gaussian surface of radius r, which shares a common center with the insulating sphere, is inflated starting from r = 0. (a) Find an expression for the electric flux passing through the surface of the gaussian sphere as a function of r for r a. (b) Find an expression for the electric flux for r a. (c) Plot the flux versus r.
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of , and the cylinder has a net charge per unit length of 2. From this information, use Gausss law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.
Two infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .
Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area. What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2? Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.
An insulating solid sphere of radius R = 6.0cm has a total positive charge Q uniformly distributed throughout its volume. The electric flux through a spherical Gaussian surface of radius r = 3.0cm is 2.26x105N.m2/C. How much charge (in units of μC) is enclosed by the Gaussian surface of radius r =3.0cm? What is the magnitude ( in units of 106N/C) of the E-field at the Gaussian surface of part (1)? What is the magnitude (in units of 106N/C) of the -field at surface of the sphere? (Example: If your answer is 3.4x106N/C, enter 3.4 in the answer box).
An insulating solid sphere of radius R = 6.0cm has a total positive charge Q uniformly distributed throughout its volume. The electric flux through a spherical Gaussian surface of radius r = 3.0cm is 2.26x105N.m2/C. How much charge (in units of μC) is enclosed by the Gaussian surface of radius r =3.0cm? What is the magnitude ( in units of 106N/C) of the E-field at the Gaussian surface of part (1)? What is the magnitude (in units of 106N/C) of the E-field at surface of the sphere?
A uniform charge density of 660 nC/m3 is distributed throughout a spherical volume of radius 6.00 cm. Consider a cubical Gaussian surface with its center at the center of the sphere. (a) What is the electric flux through this cubical surface if its edge length is 2.30 cm?___________N · m2/C(b) What is the electric flux through this cubical surface if its edge length is 17.0 cm? ___________N · m2/C
The conductive sphere of radius R +Q is concentric with a -Q charged spherical conductive shell of inner radius R1, outer radius R2, as in the figure. When r>R2, find an expression for the electric field as a function of radius r.
A uniformly charged, straight filament 8.00 m in length has a total positive charge of 2.00 µC. An uncharged cardboard cylinder 4.70 cm in length and 10.0 cm in radius surrounds the filament at its center, with the filament as the axis of the cylinder. (a) Using reasonable approximations, find the electric field at the surface of the cylinder. magnitude: ____________ kN/C direction: radially outward or radially inward? (b) Using reasonable approximations, find the total electric flux through the cylinder.
A solid conducting sphere of radius R has a uniform charge distribution, with a density = Ps * r / R where Ps is a constant and r the distance from the center of the sphere. Prove a) the total charge on the sphere is Q = πPsR ^ 3 b) the electric field of the sphere is given by E = (1 / 4πε0) * (Q / R ^ 4) * (r ^ 2)
Consider a thin-shelled hollow tube of length L, radius R with a uniform surface charge density σ and with the z-axis as its central axis. This can be described by: x2 + y2 = R2 and -L/2 ≤ z ≤ L/2. What is the electric field at z0 along the z-axis, where z0 > L/2?
Consider a nonconducting sphere and a concentric nonconducting spherical shell, shown in the figure. The inner sphere has non uniform charge density ρ1 = ρ0 / r, where ρ0 is a constant, in units of C/m2 and radius a. The outer spherical shell has uniform charge density ρ2 , inner radius b, and outer radius c. Find the magnitude of the electric field inside the inner sphere, for r < a, in terms of the given variables, as needed.