An infinitely long insulating cylinder of radius R=1.2m has a volume charge density that varies with the radius as: p(r) = Po (a - r/b) , where po=36nC/m3, a=5 and b=4 are constants, and r is the distance from the axis of the cylinder. Use Gauss' law to determine the magnitude of the electric field at r=0.4m. Take the electric constant to be ke = 8.99×10° Nm²/C2. Give your answer in N/C to the nearest 0.01N/C. In addition to entering your final numerical answer into the box, solve this problem in detail on paper. Make sure that you write your solution neatly, starting with the clear diagram and all variables on it. Make short comments/ arguments for all cancelations that you are claiming to be happening. (Explain what you are doing and why-- simply stating "it is O due to symmetry" will not suffice!)

An infinitely long insulating cylinder of radius R=1.2m has a volume charge density that varies with the radius as: p(r) = Po (a - r/b) , where po=36nC/m3, a=5 and b=4 are constants, and r is the distance from the axis of the cylinder. Use Gauss' law to determine the magnitude of the electric field at r=0.4m. Take the electric constant to be ke = 8.99×10° Nm²/C2. Give your answer in N/C to the nearest 0.01N/C. In addition to entering your final numerical answer into the box, solve this problem in detail on paper. Make sure that you write your solution neatly, starting with the clear diagram and all variables on it. Make short comments/ arguments for all cancelations that you are claiming to be happening. (Explain what you are doing and why-- simply stating "it is O due to symmetry" will not suffice!)

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 50P: An insulating solid sphere of radius a has a uniform volume charge density and carries a total...

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.
An infinitely long solid insulating cylinder of radius R has a uniform volume charge density of 0.99μC/m3. If the magnitude of the electric field 0.302m from the axis of the cylinder is 3880N/C, what is R, the radius of the cylinder, in meters? Assume that R<0.302m, so the point of observation is exterior to the cylinder.
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.
A uniform volume charge distribution ρv=5 (nC/m3) exists in a sphere that has a radius of a=3 cm. What is the magnitude of the electric field intensity at a distance R=4 cm? (Use Gauss’s Law)
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?
An electric field is found to be <3xyz, 2x2/z, x+y+z>. What is the x-component of the electric field vector at position (2, 6, 1)m?
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 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?
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as ρ = ρ0(a - (r)/(b)) where ρ0, a, and b are positive constants and r is the distance from the axis of the cylinder. Use Gauss’s law to determine the magnitude of the electric field at radial distances (a) r < R and (b) r > R.
A 3.2-cm-diameter circle lies in the yz-plane with unit vector n^ pointing in the +x-direction. What is the electric flux through the circle if the electric field is E =(2500i^−1500j^+4000k^)N/C?
The uniform charge density in an insulating sphere with a radius of 40 cm is 6*10-3 C/m3. Calculate the electric field at a distance r=20 cm from the center of the sphere using Gauss's law.