An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) = 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.

An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) = 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 59P: The volume charge density of a spherical charge distribution is given by p(r)=p0ear , where p0 , and...

See similar textbooks

Similar questions

answer is not 1.62*10^-6 and is not 4011.86 and is not 20131.55 and i will dislike of you put any of these answers and u need to give a numerical answer (not an equation with variables) otherwise i will dislike
E(r) = Bzi - ax'y'j+ (6@yxy + Bóz³) k %3D where a, B, y and & are constants and r = xi+yj+zk. Find the corresponding charge density p(r).
The electric field is defined by the equation below in rectangular coordinates. Find VA if VB is 3 volts and points A and B are located at (-1, 3, 4) m and (0, -2, 5) m respectively, in free space.
A shpere of radius R carrries a volume charge density p= pgr, where po is a constant and r is the radial distance from the centre ofthe charged sphere. The intensityofthe electric field is proportional to: (a) r? for rR (b) r for rs R and 1/r for r2 R (c) 1/r? for both r
In spherical coordinates, V = -25 volts on a conductor at r = 2 cm and V = 150 volts at re 35 cm. The space between the conductors is a dielectric for which E,= 3.12. Find the surface charge densities on the conductors.
A charged sphere of radius Rohas charge density p=p,. Find the total charge in the sphere.
Let k denote 1/47eg. The magnitude of the electric field at a distance r from an isolated point‏particle with charge q is:‏
The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs 1.0 m; p(r)= Po(1-4r/3) For r> 1.0 m; p(r)= 0, where r is in meters. What is the value of r in meters for which the electric field is maximum?
A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where Bis a constant, and ris the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ - BA So we can write this as dq = dv But. dV = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B =
This ain't graded this is from a module study
The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant. (a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?b) Calculate the electric field for a point outside the cylinder, r > Rc) Calculate the electric field for a point inside the cylinder, r<R.d) Sketch Exr
Please solve asap and explain how you reached that solution properly. Thank you in advance!