2-аxis х-ахis Problem 4: A point charge of Q = 45 µC is located at the origin. A hollow cylinder of radius R= 15 cm and height H= 17 cm is concentric with the z-axis with one end at z = 0. Refer to the figure. The x-axis points out of the screen. H R у-ахis Part (a) Consider an arbitrary point on the cylindrical surface at height z. Enter an expression for the component of the electric field perpendicular to the surface at that point. Give your answer in terms of R, z, Q, and the Coulomb constant k. E = Part (b) Imagine breaking up the cylindrical surface by slicing it horizontally into infinitesimal rings, each of width dz. Consider such a ring located at height z above the x-y plane. Enter an expression for the differential of the electric flux through the ring in terms of defined quantities. dp = Part (c) Integrate the electric flux over the height of the cylinder (from z = 0 to z = H) and enter an expression for the electric flux through the cylindrical surface in terms of defined quantities.

2-аxis х-ахis Problem 4: A point charge of Q = 45 µC is located at the origin. A hollow cylinder of radius R= 15 cm and height H= 17 cm is concentric with the z-axis with one end at z = 0. Refer to the figure. The x-axis points out of the screen. H R у-ахis Part (a) Consider an arbitrary point on the cylindrical surface at height z. Enter an expression for the component of the electric field perpendicular to the surface at that point. Give your answer in terms of R, z, Q, and the Coulomb constant k. E = Part (b) Imagine breaking up the cylindrical surface by slicing it horizontally into infinitesimal rings, each of width dz. Consider such a ring located at height z above the x-y plane. Enter an expression for the differential of the electric flux through the ring in terms of defined quantities. dp = Part (c) Integrate the electric flux over the height of the cylinder (from z = 0 to z = H) and enter an expression for the electric flux through the cylindrical surface in terms of defined quantities.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

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P4E5

х-ахis
2-аxis
Problem 4: A point charge of Q = 45 µC is located at the origin. A hollow cylinder of radius
R = 15 cm and height H = 17 cm is concentric with the z-axis with one end at z = 0. Refer to the
figure. The x-axis points out of the screen.
H
R
у-аxis
Part (a) Consider an arbitrary point on the cylindrical surface at height z. Enter an expression for the component of the electric field perpendicular to
the surface at that point. Give your answer in terms of R, z, Q, and the Coulomb constant k.
E =
Part (b) Imagine breaking up the cylindrical surface by slicing it horizontally into infinitesimal rings, each of width dz. Consider such a ring located
at height z above the x-y plane. Enter an expression for the differential of the electric flux through the ring in terms of defined quantities.
d =
Part (c) Integrate the electric flux over the height of the cylinder (from z = 0 to z = H) and enter an expression for the electric flux through the
cylindrical surface in terms of defined quantities.
Ф

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