3. A solid glass sphere of radius a contains excess charge distributed throughout its volume such that the volume charge density depends on the distance r from the sphere's center according to the equation p (t) = p.(r/a) where p, is a constant. (a) What are the units of p ? (b) Compute the total charge Q on the sphere. (c) Determine the magnitude of the electric fjeld for 1) r< a' (ii) r 2 a Write your answers to both (i) and (ii) in terms of Q, a, r, and fundamental constants. (d) Sketch the electric field magnitude E as a function of r on the graph below. Be sure to indicate on the vertical axis the value of E at r = a. E

3. A solid glass sphere of radius a contains excess charge distributed throughout its volume such that the volume charge density depends on the distance r from the sphere's center according to the equation p (t) = p.(r/a) where p, is a constant. (a) What are the units of p ? (b) Compute the total charge Q on the sphere. (c) Determine the magnitude of the electric fjeld for 1) r< a' (ii) r 2 a Write your answers to both (i) and (ii) in terms of Q, a, r, and fundamental constants. (d) Sketch the electric field magnitude E as a function of r on the graph below. Be sure to indicate on the vertical axis the value of E at r = a. E

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

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)?
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 .
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?
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.
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.
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.
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 volume charge density of a sphere of Radius R is directly related to the radius of the sphere as given by the equation p(r) = br where b is a positive integer. What would be expression for the electric field at r = 1/2 R 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)
Two concentric spherical shells with radius “R1” and “R2” , charge quantity “Q1” and “Q2” respectively, find the distribution of electric field strength in space , and make the E-r relationship curve.
An infinitely long solid cylinder of radius 17 cm has a non-uniform volume charge density given by ρ (rho) = 4r3 where ρ (rho) is in C/m3 when r is in meters. a) Calculate the magnitude of the electric field at a distance of 8 cm from the axis of the cylinder. b) Calculate the magnitude of the electric field at a distance of 30 cm from the axis of the cylinder.
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.