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 = a and extends to x = 2a. The linear charge density is λ = b/x3 where b is a constant. Determine the electric field at the origin.
A line of charge starts at x=+x0 and extends to positive infinity. The linear charge density is λ=λ 0 x0 /x,where λ 0 is a constant. Determine the electric field at the origin.
A continuous line of charge lies along the x axis, extending from x = + x0 to positive infinity. The line carries charge with a uniform linear charge density λ0. What are the magnitude and direction of the electric field at the origin?
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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- Point P sets above an infinite line of charge 2 m in the positive z direction. The line of charge itself has a charge density ? of -5.0 x 10⁶ C/m. What is the magnitude of the electric field at point P?arrow_forwardTwo homogeneous rods with a length of 5 cm each are positioned as in Fig. a. Determine the magnitude and direction of the electric field vector at point P on the coordinates (5.0) cm, if the unit charge density is λ = 2.10-9 C / m! b. If an electron is placed at point P, what is the electric force that is experienced by the electron?arrow_forwardPositive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, r, and and appropriate constants. Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q, q, a, r, and appropriate constants. Calculate the direction of the force that the charge distribution Q exerts on q.arrow_forward
- Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, r, and and appropriate constants. Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, and appropriate constants. Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q, q, a, r, and appropriate constants. Calculate the direction of the force that the charge distribution Q exerts on q.arrow_forwardPositive 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. b) Determine the electric field, E(r), for r > R (outside the sphere). c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere (r = R)? d) What is the energy stored in this electric charge configuration?arrow_forwardA continuous line of charge lies along the x axis, extending from x = +x0 to positive infinity. The line carries positive charge with a uniform linear charge density λ0. What are (a) the magnitude and (b) the direction of the electric field at the origin?arrow_forward
- 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.arrow_forwardThe 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_forward
- You are working as an intern for a meteorological laboratory. You are out in the field taking measurements with a device that measures electric fields. You measure the electric field in the air immediately above the Earth's surface to be 139 N/C directed downward. (Assume the radius of the Earth is 6.37 x 106 m.) (a) Determine the surface charge density (in C/m²) on the ground. C/m? (b) Imagine the surface charge density is uniform over the planet. Determine the charge (in C) of the whole surface of the Earth. (e) Determine the Earth's electric potential (in V) due to the charge found in (b). V (d) Determine the difference in potential (in V) between the head and the feet of a person 1.50 m tall. (Ignore any charges in the atmosphere.) Varrow_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_forward
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