A solid nonconducting sphere of radius R = 6.7 cm has a nonuniform charge distribution of volume charge density ρ = (16.7 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/2.0, and (d) r = R?

A solid nonconducting sphere of radius R = 6.7 cm has a nonuniform charge distribution of volume charge density ρ = (16.7 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/2.0, and (d) r = R?

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

A sphere of radius R=0.255 m and uniform charge density −151 nC/m3 lies at the center of a spherical, conducting shell of inner and outer radii 3.50⁢R and 4.00⁢R, respectively. If the conducting shell carries a total charge of Q=14.3 nC, find the magnitude of the electric field at the given radial distances from the center of the charge distribution. 0.360R: ? 3.60⁢R: ? 3.40R: ?
A long, nonconducting, solid cylinder of radius 4.0 cm has a nonuniform volume charge density r that is a function of radial distance r from the cylinder axis: r =Ar2. For A = 2.5 mC/m5, what is the magnitude of the electric field at (a) r = 3.0 cm and (b) r = 5.0 cm?
A solid sphere of insulating material with radius R=7.62cm�=7.62cm has a uniform volume charge density given by p(r) = { (p0 for r<=R), (0 for r > R)} where ρ0=296nC/m3. What is the magnitude, in newtons per coulomb, of the electric field at a distance r=3.28cm from the center of the sphere. What is the magnitude, in newtons per coulomb, of the electric field at a distance r=11.9cm from the center of the sphere.
A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r 1 = 6R the electric field has a magnitude E 0. What is the magnitude of the electric field at a radial distance r 2 = R/6 as a multiple of E 0 ?
A solid ball of radius R has a uniform volume charge density and produces a certain electric field magnitude E1 at point P, a distance 3.08R from the ball's center. If a core of radius 0.385R is removed from the ball, what fraction of E1 will the field magnitude at P be?
Charge of uniform volume density r = 3.2 mC/m3 fills a nonconducting solid sphere of radius 5.0 cm.What is the magnitude of the electric field (a) 3.5 cm and (b) 8.0 cm from the sphere’s center?
A sphere of radius R=0.250 m and uniform charge density −151 nC/m3 lies at the center of a spherical, conducting shell of inner and outer radii 3.50R and 4.00R, respectively. If the conducting shell carries a total charge of Q=−64.3 nC, find the magnitude of the electric field at the given radial distances from the center of the charge distribution. 0.460R= ?N/C 3.55R= ?N/C 2.00R= ?N/C 5.50R= ?N/C
A solid nonconducting sphere of radius R = 6.7 cm has a nonuniform charge distribution of volume charge density ρ = (16.7 pC/m3)r/R, where r is radial distance from the sphere's center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r = 0, (c) r = R/2.0, and (d) r = R?
A hollow conducting sphere with inner radius R and outer radius 2R has a non-uniform volume charge distribution in the region R<r<2R given by ρ(r)=(4C/m⁵)r². If R=0.564m, what is the magnitude of the electric field (in N/C) at r=3/2R?
A spherical Conductor of radius 0.330 m has a spherical cavity of radius 0.120m at its center. The conductor carries a total charge of -6.00 nC; in addition, at the center of the spherical cavity is a point charge of +4.00 nC. Find (a) the total charge on the surface of the cavity, (b) the total charge on the outer surface of the condutor, (c) the magnitude of the electric field just inside te surface of the cavity, and (d) the magnitude of the electric field just outside the outer surface of the conductor.
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.
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.