Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 23, Problem 39AP
To determine
The electric field at the origin.
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A line of charge starts at x = +x0 and extends to positive infinity. The linear charge density is λ = λ0x0/x, where λ0 is a constant. Determine the electric field at the origin.
Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric
field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere.
a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p.
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Charge is distributed throughout a spherical volume of radius R with a density ρ = αr2, where α is a constant. Determine the electric field due to the charge at points both inside and outside the sphere.
Chapter 23 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 23.2 - Suppose a point charge is located at the center of...Ch. 23.3 - If the net flux through a gaussian surface is...Ch. 23 - A negatively charged rod of finite length carries...Ch. 23 - A positively charged disk has a uniform charge per...Ch. 23 - A uniformly charged ring of radius 10.0 cm has a...Ch. 23 - The electric field along the axis of a uniformly...Ch. 23 - Example 23.3 derives the exact expression for the...Ch. 23 - A uniformly charged rod of length L and total...Ch. 23 - A continuous line of charge lies along the x axis,...Ch. 23 - A thin rod of length and uniform charge per unit...
Ch. 23 - (a) Consider a uniformly charged, thin-walled,...Ch. 23 - A vertical electric field of magnitude 2.00 104...Ch. 23 - A flat surface of area 3.20 m2 is rotated in a...Ch. 23 - A nonuniform electric field is given by the...Ch. 23 - An uncharged, nonconducting, hollow sphere of...Ch. 23 - Find the net electric flux through the spherical...Ch. 23 - Four closed surfaces, S1 through S4 together with...Ch. 23 - A charge of 170 C is at the center of a cube of...Ch. 23 - (a) Find the net electric flux through the cube...Ch. 23 - A particle with charge of 12.0 C is placed at the...Ch. 23 - A particle with charge Q = 5.00 C is located at...Ch. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Find the net electric flux through (a) the closed...Ch. 23 - Figure P23.23 represents the top view of a cubic...Ch. 23 - Determine the magnitude of the electric field at...Ch. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - A large, flat, horizontal sheet of charge has a...Ch. 23 - A nonconducting wall carries charge with a uniform...Ch. 23 - A uniformly charged, straight filament 7.00 m in...Ch. 23 - You are working on a laboratory device that...Ch. 23 - Consider a long, cylindrical charge distribution...Ch. 23 - Assume the magnitude of the electric field on each...Ch. 23 - A solid sphere of radius 40.0 cm has a total...Ch. 23 - A cylindrical shell of radius 7.00 cm and length...Ch. 23 - You are working for the summer at a research...Ch. 23 - You are working for the summer at a research...Ch. 23 - Find the electric flux through the plane surface...Ch. 23 - Prob. 38APCh. 23 - Prob. 39APCh. 23 - Show that the maximum magnitude Emax of the...Ch. 23 - A line of positive charge is formed into a...Ch. 23 - Prob. 42APCh. 23 - A sphere of radius R = 1.00 m surrounds a particle...Ch. 23 - A sphere of radius R surrounds a particle with...Ch. 23 - A slab of insulating material has a nonuniform...Ch. 23 - A sphere of radius 2a is made of a nonconducting...Ch. 23 - Prob. 47CPCh. 23 - Prob. 48CPCh. 23 - Review. A slab of insulating material (infinite in...Ch. 23 - Identical thin rods of length 2a carry equal...Ch. 23 - A solid insulating sphere of radius R has a...
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- The electric field everywhere on the surface of a thin, spherical shell of radius 0.775 m is of magnitude 897 N/C and points radially toward the center of the sphere. (a) What is the net charge within the sphere's surface? X If the net charge inside the sphere is moved to the center of the sphere would this change the value of the electric field on the surface? nC (b) What is the distribution of the charge inside the spherical shell? O The negative charge has an asymmetric charge distribution. O The positive charge has a spherically symmetric charge distribution. The negative charge has a spherically symmetric charge distribution. O The positive charge has an asymmetric charge distribution. 4arrow_forwardTwo bidirectionally infinite line charges exist in vacuum. One has a charge density of -8 nC/m at x = -6, y = -3, while the other has a charge density of 6 nC/m at y = -8, z = -1. Determine the y-component of the electric field in V/m at (7, 7, 3). All coordinates are measured in meters.arrow_forwardCharge of a uniform density (7 pC/m2) is distributed over the entire xy plane. A charge of uniform density (10 pC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.arrow_forward
- +X, to positive infinity. The line carries positive charge with a uniform linear charge density Ao. A continuous line of charge lies along the x axis, extending from x = (a) What is the magnitude of the electric field at the origin? (Use the following as necessary: 1o, xo, and ke.) 0. %3D (b) What is the direction of the electric field at the origin? O +X +y O -zarrow_forwardCharge of a uniform density (11 pC/m?) is distributed over the entire xy plane. A charge of uniform density (6 pC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.arrow_forwardhelparrow_forward
- d 00 = A semicircular wire of radius R is uniformly charged with Q₁ -0.3Q and located in a two dimensional coordinate system as shown in the figure. A point charge Q2-9Q is placed at 0.36 R on the y-axis. Determine the electric field at point o in terms of kQ/R2F where f is the unit vector. Take mt=3.14 and provide your answer with two decimal places Answer: Q₁ Q₂ R 0arrow_forwardCharge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude 840 N/C. The charge density is calulated as: p = 2.2×10−6 Cm3 What is the magnitude of the electric field at a distance of 2.00 cm from the sphere's center?arrow_forwardThe electric field E = C₁ấz + c₂ấy + c3ẩ₂ V/m at point P(0, 1, 0) given a point charge of 3 nC at the origin, a line charge distribution of 8 nC/m at x = 4, y = −3, and a plane charge of 0.5 nC/m² at z = 5. All coordinates are given in meters. Assume free space. What is the numerical value of c₁? What is the numerical value of c₂? What is the numerical value of c3?arrow_forward
- The figure gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es = 4.3 × 107 N/C. What is the charge on the sphere?arrow_forwardA total charge of Q is uniformly distributed along a line, which extends along the x- axis from x=0 to x=L. What is the electric field due to this line of charge at a point P, which is on the x axis at x=a. Your answer should be a symbolic expression that only depends on the variables k, Q, a, and L. What does your expression reduce to when a≫L (far-field limit)?arrow_forwardPositive electric charge is uniformly distributed along the y-axis with a linear charge density l. Consider the case where charge is distributed only between points y = +a and y = -a. For points between the +x-axis, graph the x-component of the electric field as a function of x, Ex (x), for values x = a/2 and x = 4a. Consider instead the case where charge is distributed along the entire y-axis with the same charge density l. Using the same graph as in part (a), plot the x-component of the electric field, Ex (x), as function of x for values of x between x = a/2 and x = 4a.arrow_forward
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