Consider a line charge of infinite extent in the Z direction with charge density λ =λ0/(1 + ( Z/a)2) where λ0 is a positive constant • a) What is the total charge Q enclosed by an imaginary Gaussian surface of radius r? • b) What is the electric flux through this surface due to the line charge?

Consider a line charge of infinite extent in the Z direction with charge density λ =λ0/(1 + ( Z/a)2) where λ0 is a positive constant • a) What is the total charge Q enclosed by an imaginary Gaussian surface of radius r? • b) What is the electric flux through this surface due to the line charge?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter5: Electric Charges And Fields

Section: Chapter Questions

Problem 123AP: Calculate the electric field due to a uniformly charged rod of length L, aligned with the x-axis...

See similar textbooks

Similar questions

Show that the following expression for the electric field a distance z along the central axis of a thin ring of continuous positive charge is correct. Derive the expression based upon the geometry shown in the diagram below. Let q-total charge of the ring, R=radius of ring. Be sure to state the magnitude and direction of the electric field at the point P.
The total electric field at point P, a distance x from the center of a ring of radius a, is given by the following equation. Substituting the given values for the charge and radius, we have the following.
A charged semicircular ring of radius a extending from φ = π to φ = 2π lies in the xy plane and is centred atthe origin. If the charge distribution is a sin φ, calculate the electric field intensity at P(0, 0, h).
Calculate the electric field due to a uniformly charged rod of length L, aligned with the x-axis with one end at the origin; at a point P on the z-axis.
Example 23.3 derives the exact expression for the electric field at a point on the axis of a uniformly charged disk. Consider a disk of radius R = 3.00 cm having a uniformly distributed charge of +5.20 C. (a) Using the result of Example 23.3, compute the electric field at a point on the axis and 3.00 mm from the center. (b) What If? Explain how the answer to part (a) compares with the field computed from the near-field approximation E = /20. (We derived this expression in Example 23.3.) (c) Using the result of Example 23.3, compute the electric field at a point on the axis and 30.0 cm from the center of the disk. (d) What If? Explain how the answer to part (c) compares with the electric field obtained by treating the disk as a +5.20-C charged particle at a distance of 30.0 cm.
If more electric field lines leave a gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?
A 10cm10cm piece of aluminum foil of 0.1 mm thickness has a charge of that spreads on both wide side surfaces evenly. You may ignore the charges on the thin sides of the edges. (a) Find the charge density. (b) Find the electric field 1 cm from the center, assuring approximate planar symmetry.
A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and –Q, respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) r < a; (b) a < r < b; and (c) r > b.
The figure shows two concentric rings, with radii R and R' =3R, lying on the same plane. Point P is located on the Z axis at a distance D=2.00R from the center of the rings. The charge on the outer ring (of radius R') is Q=5.00µC and the net electric field at point P is zero. The charge on the inner ring (of radius R) is:______µC. (express your answer to 3 significant figures).
Two concentric rings, of radii R and 2R, lie on the y-z plane and at the origin as shown in the figure. Point P lies on the x axis, at x = 2R. Both rings contain uniformly distributed charges. The charge on the inner ring is Q. What is the total charge on the outer ring if the net electric field at point P is zero?
A conducting sphere of radiusais placed at the origin surrounded by a spherical conductingshell of inner radiusband outer radiusc. The sphere carries a charge of−3Qwhile the outershell is charged to 2Q. Use Gauss Law to find E of the following: c) inside the shell (b < r < c) d) outside the shell (r > c)
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r < a. (b) From this value, find the magnitude of the electric field for r < a. (c) What charge is contained within a sphere of radius r when a < r < b? (d) From this value, find the magnitude of the electric field for r when a < r < b. (e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r ? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these…