As shown in the figure below, you have a hollow spherical shell of radius R with a total charge uniformly spread over its surface. At the center of this hollow sphere is a point charge 2Q. (a) Find an expression for the electric field E(r) in every region. Make sure to include the direction of the vector! (b) Draw a graph of the magnitude of the electric field as a function of distance r from the central charge. Make sure to label your axes, and be as accurate as you can! (c) Find an expression for the electric potential at the surface of the shell (r = R). %3D

As shown in the figure below, you have a hollow spherical shell of radius R with a total charge uniformly spread over its surface. At the center of this hollow sphere is a point charge 2Q. (a) Find an expression for the electric field E(r) in every region. Make sure to include the direction of the vector! (b) Draw a graph of the magnitude of the electric field as a function of distance r from the central charge. Make sure to label your axes, and be as accurate as you can! (c) Find an expression for the electric potential at the surface of the shell (r = R). %3D

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

See similar textbooks

Similar questions

Recall that in the example of a uniform charged sphere, p0=Q/(43R3). Rewrite the answers in terms of the total charge Q on the sphere.
The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r 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.
What is the magnitude of the electric field just above the middle of a large, flat, horizontal sheet carrying a charge density of 98.0 nC/m2?
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.
Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a half-circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?
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.
This equation is for the electric field of a uniform ring which is charged and is at point z which is perpendicular to the center of the ring. (it means z=0 is part of the plane in which the ring is in). R=radius of ring, Q= total charge of ring, k= coulomb's constant. If k=1 units, Q=1 units, R=8 units, what is Ering, z when z=6 units?
An infinite line charge has constant charge-per-unit-length λ. Surrounding the line charge is a cylindrical shell of radius R, and carrying a constant charge-per-unit area σ. Given λ, what must σ be in order to get 0 electric field for all points outside the cylindrical shell? For that σ, what is the electrical field in between the line of charge and shell?
the figure shows a solid sphere of total charge Q and radius R. Inside the sphere is a gaussian surface with radius r and it encloses charge q. use the definition of volumetric charge density to find the ratio of q/Q
Two very long lines of charge are parallel to each other. One with a linear charge density −λ−λ , and the other have the linear charge density +λ+λ, and they are separated by a distance RR as shown in the figure. Calculate the electric field at a point half-way between the lines of charge. r⃗ r→ is the unit radial vector in the cylindrical coordinate of the line with +λ+λ charge density.
A uniformly charged sphere, made of insulating material, has a radius a and a total charge of 2Q. The sphere is concentric with a conducting spherical shell that has inner radius b and outer radius c. (see figure). The shell has charge of 2Q as wella) Using Gauss’s Law, and with adequate explanation, derive an expression for the electric field inside the sphere, r<a)b) Using Gauss’s Law, and with adequate explanation derive an expression for the electric field outside the sphere, but before the inner surface of the shell a<r<b)c) Using Gauss’s Law, and with adequate explanation derive an expression for the electric field inside the metalshell, b<r<cd) Using Gauss’s Law, and with adequate explanation derive an expression for the electric field outside the metal shell, r>c,e) What is the charge on the inner surface of the metal shell? explain