An infinitely-long solid cylinder of radius R is filled with a uniform volume density of charge p. Calculate the electric field inside the cylinder, at a distance r from the centerline (r < R, of course), using the following steps: sketch a diagram, and briefly indicate what you know about the electric field from symmetry; choose as a gaussian surface a cylinder of length L and radius r (sketch it on your diagram), and show, in detail, that the flux through it is 2rrLE; calculate the charge inside, apply Gauss's Law, and simplify.

An infinitely-long solid cylinder of radius R is filled with a uniform volume density of charge p. Calculate the electric field inside the cylinder, at a distance r from the centerline (r < R, of course), using the following steps: sketch a diagram, and briefly indicate what you know about the electric field from symmetry; choose as a gaussian surface a cylinder of length L and radius r (sketch it on your diagram), and show, in detail, that the flux through it is 2rrLE; calculate the charge inside, apply Gauss's Law, and simplify.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 54P: Charge is distributed throughout a very long cylindrical volume of radius R such that the charge...

See similar textbooks

Similar questions

Consider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.
Determine the electric field at a distance `d` to the right of a thin-walled cylindrical shell with uniform distributed charge (See attached image). Provided are: the total charge `Q`, radius `R`, and shell length `h`. I can compute most of the solution, however, I don't understand the integration limits (See attached image). Given that the point on which I'm calculating the electric field is on the right side of the shell, shouldn't I be integrating from `d + h` to `d` instead of the other way around? If not, why?
Figure shows six pointcharges that all lie in the same plane. FiveGaussian surfaces – S1, S2, S3, S3, S4 and S5, -each enclose part of this plane, and Fig. 7 showsthe intersection of each surface with the plane.Rank these five surfaces in order of the electricflux through them, from most positive to mostnegative. Show your solution.
You measure the excess charge on a hollow conductor (shown right) to be -5.5 μC, and a 3.5-μC point charge is placed inside the cavity. What's the total charge on the inside surface of the conductor in μC?
A thin, circular plate of radius B, uniform surface charge density, and total charge Q, is centered on the origin and lies in the x-y plane. What is the electric flux ΦE through a sphere of radius r, also centered on the origin, as a function of r? Consider both (a.) r > B and (b.) r < B:
Consider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and aradius, r. Derive an equation for the magnitude of the electric field at the point, P, at the centercurvature of the rod, as shown in the figure below. Write the final answer in terms of λ and r, and simplify your answer as much as possible.
Find the electric field a distance z above the center of a flat circular disk of radius R (See attatched figure) that carries a uniform surface charge σ. What does your formula give in the limit R → ∞? Also check the case z >> R.
Reformulate Gauss's law by choosing the unit normal of the Gaussian surface to be the one directed inward.
Consider a uniform electric field of E = (a, b, 0) and a disk of radius R What is the flux through the disk if it sits in the yz-plane? What is the flux through the disk if it sits in the xy-plane? What is the maximum flux through the disk as it rotated through all possible orientations?
Determine the total charge distribution on r = b, and on r = a., explain Check if the electrical field for this configuration match the findings that for all points r inside the circle r<a is E= q/4piΕor2 and for all points r outside the shell r>a is E=0
A total charge Q is distributed uniformly throughout a spherical volume that is centered at o1 and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at o2 (see below). Show that the electric field everywhere in the empty region is given by E=Qr40R3 where r is the displacement vector directed from o1 to o2 .
A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.