Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 5.2, Problem 3eT
When
By what trigonometric function of
Rewrite the quantity described above as a product of just the vectors
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A thin rod is bent into a circular arc that subtends an angle 2θ of a circle centered at P. A total charge, Q, is distributed uniformly over the full rod. Let the positive x direction be towards the right of the page, and the positive y direction is towards the top of the page.
In Cartesian unit-vector format, what is the electric field at P?
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.
Consider two concentric insulating cylinders of infinite length. The inner
cylinder is solid with radius
R, while the outer cylinder is a hollow shell with inner radius a and outer radius b. Both cylinders have the same volume charge density of +ρ. Using Gauss’s Law, find the electric field as a function of r (where r= 0 at the central axis) in the interval a≤r < b.
Note:
Your final equation should be in terms of given parameters of ρ,a,b,R, and r.
Chapter 5 Solutions
Tutorials in Introductory Physics
Ch. 5.1 - Press a piece of sticky tape, about 15-20 cm in...Ch. 5.1 - B. Make another piece of tape a described above....Ch. 5.1 - Each member of your group should press a tape onto...Ch. 5.1 - Obtain an acrylic rod and a piece of wool or fur....Ch. 5.1 - Base your answers to the following questions on...Ch. 5.1 - Two positive point charges +q and +Q (with Qq )...Ch. 5.1 - Two more +Q charges are held in place the same...Ch. 5.1 - Rank the four cases below according to the...Ch. 5.1 - Charge an acrylic rod by rubbing it with wool....Ch. 5.1 - Hold the charges rod horizontally. Use a charges...
Ch. 5.1 - Imagine that two charged rods are held together as...Ch. 5.1 - Five short segments (labeled 1-5) of acrylic rod...Ch. 5.1 - In case A at right, a point Charge +q is a...Ch. 5.1 - A small ball with zero net charge is positively...Ch. 5.1 - Hang an uncharged metal or metal-covered ball from...Ch. 5.1 - The situation in part A suggests a way to think...Ch. 5.2 - Hold a small piece of paper (e.g., an index card)...Ch. 5.2 - The area of a flat surface can be represented by a...Ch. 5.2 - Place a large piece of graph paper flat on the...Ch. 5.2 - Fold the graph paper twice so that it forms a...Ch. 5.2 - Form the graph paper into a tube as shown. Can the...Ch. 5.2 - What must be true about a surface or a portion of...Ch. 5.2 - In the tutorial Charge, you explored the region...Ch. 5.2 - Suppose that the charge, qtest , on the pith ball...Ch. 5.2 - The quantity F/qtest evaluated at any point is...Ch. 5.2 - Sketch vectors at each of the marked points to...Ch. 5.2 - The diagram at right shows a two-dimensional top...Ch. 5.2 - Compare the magnitude of the electric field at...Ch. 5.2 - Obtain a wire loop. The Loop represents the...Ch. 5.2 - For a given surface, the electric flux, E , is...Ch. 5.2 - You will now examine the relationship between the...Ch. 5.2 - When EandA were parallel, we called the quantity...Ch. 5.3 - In the following Questions, a Gaussian cylinder...Ch. 5.3 - In the following Questions, a Gaussian cylinder...Ch. 5.3 - In the following Questions, a Gaussian cylinder...Ch. 5.3 - In the following Questions, a Gaussian cylinder...Ch. 5.3 - Are your answer to part A-C of section I...Ch. 5.3 - In part D of section I, you tried to determine the...Ch. 5.3 - Find the net flux through each of the Gaussian...Ch. 5.3 - The three spherical Gaussian surfaces at right...Ch. 5.3 - A large sheet has charge density +o . A...Ch. 5.3 - The Gaussian cylinder below encloses a portion of...Ch. 5.4 - Suppose an object moves under the influence of a...Ch. 5.4 - An object travels from point A to point B while...Ch. 5.4 - An object travels from point A to point B while...Ch. 5.4 - State the work-energy theorem in your own words....Ch. 5.4 - Draw electric field vectors at point W, X, Y, and...Ch. 5.4 - A particle with charge +qo , travels along a...Ch. 5.4 - The particle travels from point X to point Z along...Ch. 5.4 - Suppose the particle travels from point W to point...Ch. 5.4 - Compare the work done as the particle travels from...Ch. 5.4 - Suppose the charge of the particle in section II...Ch. 5.4 - Shown at right are four Points near a positively...Ch. 5.5 - A small portion near the center of a large thin...Ch. 5.5 - Use the principle of superposition to determine...Ch. 5.5 - Use the principle of superposition to determine...Ch. 5.5 - Consider instead a portion near the center of a...Ch. 5.5 - A second plate with the same magnitude charge as...Ch. 5.5 - The inner surface of one plate has a uniform...Ch. 5.5 - B. Suppose the plates are discharged, then held a...Ch. 5.5 - Compare the ratio QV that you calculated for two...Ch. 5.5 - For the following cases, state whether each of the...
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