A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant.What is the volume density r of the charge distribution?

A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant.What is the volume density r of the charge distribution?

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 49PQ

See similar textbooks

Similar questions

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 .
The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?
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.
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.
A spherical ball of charged particles has a uniform charge density. In terms of the ball’s radius R, at what radial distances (a) inside and (b) outside the ball is the magnitude of the ball’s electric field equal to of the maximum magnitude of that field?
If a solid insulating sphere of radius 50 cm carries a total charge of 150 µC uniformly distributedthroughout its volume, what is its a) volume charge density? What is the magnitude of the electricfield at b) 10 cm and c) 65 cm from the center of the sphere.
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?
In Figure 2, a sphere of radius r = 0.42 m carries a uniform volume charge density of rho = 2.3 × 10^-10 C/m^2. A spherical cavity of radius 0.21 m is then cut out and left empty as shown in the figure. Points A and C are the centers of the sphere and the spherical cavity, respectively. Find the magnitude and direction of the electric field at point B.
1.Charge is uniformly distributed around a ring of radius R = 2.40 cm, and the resulting electric field magnitude E is measured along the ring's central axis (perpendicular to the plane of the ring).At what distance from the ring's center is E maximum?
A charge of uniform linear density 2.00 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.60 cm, outer radius = 10.6 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 15.2 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?