Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 19.2, Problem 1bTH
Consider an imaginary surface in a uniform electric field
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The figure shows a sphere carrying a uniformly distributed volume charge Q. Three Gaussian surfaces are concentric with the sphere as shown.
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Apply Gauss’s law to find the magnitude of the electric field in the region r < a. Inthe figure, draw the Gaussian surface you are using, and indicate on that surface the direction of anyvectors which appear in the mathematical expression of Gauss’s law. Express your answer in terms ofa, Q, r, and ε0. (If you get an expression involving ρ, substitute it from above to re-express youranswer in terms of the stated variables.)
Chapter 19 Solutions
Tutorials in Introductory Physics
Ch. 19.1 - Draw a separate free-body diagram for each ball....Ch. 19.1 - Suppose the charge on the second ball is reduced...Ch. 19.1 - Predict what will happen if the net charge on ball...Ch. 19.1 - How does Coulomb’s law apply to situations in...Ch. 19.1 - In cases A and B shown at right there are two...Ch. 19.1 - In case C, two positive point charges +2Q are each...Ch. 19.1 - In case E a positive point charge with +Q is a...Ch. 19.1 - Is the magnitude of FPgreater than, less than, or...Ch. 19.1 - Is the magnitude of the net force on +qgreater...Ch. 19.1 - A second negative point charge Q is placed as...
Ch. 19.1 - A thin semicircular rod like the one in problem 4...Ch. 19.1 - Sketch the charge distribution on the rod.Ch. 19.1 - Is there a non-zero net electric force on the rod?...Ch. 19.1 - Is there a non-zero net electric force on the...Ch. 19.1 - State whether the magnitude of the net electric...Ch. 19.2 - Prob. 1aTHCh. 19.2 - Consider an imaginary surface in a uniform...Ch. 19.2 - Write an expression for the net electric flux net...Ch. 19.2 - Prob. 2aTHCh. 19.2 - Prob. 2bTHCh. 19.2 - Consider the surface element A itself as composed...Ch. 19.2 - Consider the left side of the box as Consisting of...Ch. 19.2 - The loop is held to the right of a positive point...Ch. 19.2 - Prob. 3bTHCh. 19.2 - Suppose that the new charge located to the right...Ch. 19.3 - Prob. 1aTHCh. 19.3 - Prob. 1bTHCh. 19.3 - Suppose that the curved portion of the Gaussian...Ch. 19.3 - A Second point charge +q is placed to the right of...Ch. 19.3 - Sketch a vector at each of points AD to represent...Ch. 19.3 - Sketch a vector at each of points AD to represent...Ch. 19.3 - Sketch a vector at each of points AD to represent...Ch. 19.3 - Sketch the net electric field at each of points...Ch. 19.3 - Calculate the magnitude of the electric field at...Ch. 19.4 - A small test charge qo travels from point X to...Ch. 19.4 - Prob. 1bTHCh. 19.4 - Points B and C are a distance ro away from the...Ch. 19.4 - A large metal sphere with zero net charge is now...Ch. 19.4 - Draw arrows on the diagram to indicate the...Ch. 19.4 - A positively charged test particle moves from...Ch. 19.4 - A positively charged test particle moves from A to...Ch. 19.4 - Find the magnitude and direction of the electric...Ch. 19.4 - A particle of mass mo and charge qo is released...Ch. 19.5 - The Surface area of the face of each plate is AI ....Ch. 19.5 - A new capacitor is formed by attaching two...Ch. 19.5 - Find the charge density on the plates. Explain.Ch. 19.5 - Find the electric potential difference between the...Ch. 19.5 - Show that the capacitance of the enlarged plates...
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- A cubical gaussian surface is bisected by a large sheet of charge, parallel to its top and bottom faces. No other charges are nearby. (i) Over how many of the cubes faces is the electric field zero? (a) 0 (b) 2 (c) 4 (d) 6 (ii) Through how many of the cubes faces is the electric flux zero? Choose from the same possibilities as in part (i).arrow_forwardConsider a plane surface in a uniform electric field as in the Figure , where cm and . If the net flux through the surface is 6.00 Nm2/C, find the magnitude of the electric field.arrow_forwardA uniform electric field measured over a square surface with side length d = 15.5 cm makes an angle θ = 67.0° with a line normal to that surface, as shown in the figure below. There is a square horizontal surface with length and width d. The surface has a normal vertical axis at the center with a vector labeled vector E traveling from the center of the plane up and to the right. Vector E and the normal vertical axis form an angle labeled θ. If the net flux through the square is 5.40 N · m2/C, what is the magnitude Eof the electric field (in N/C)? N/Carrow_forward
- The Gaussian cylinder is in a uniform electric field of magnitude E, aligned with the cylinder axis. Find the sign and magnitude of the flux through: Surface A: Surface B: Surface C: Is the net flux through the Gaussian surface positive, negative, or zero?arrow_forwardConsider the uniform electric field →E=(4300 j+ 2800 k) NC. What is its electric flux through a circular area of radius 2.4 m that lies in the xy-plane?arrow_forwardThe figure shows three Gaussian surfaces and the electric flux through each. What is the charge on q1, q2, and q3. express your answers as a multiple of q.arrow_forward
- Calculate the absolute value of the electric flux for the following situations (In all case provide your answer in N m2/C): c. A uniform electric field E = (−350 i + 350 j + 350 k) N/C through a disk of radius 3 cm in the x-z plane.arrow_forwardA cylinder of diameter 1.72 m is in a region where the electric field is as shown in the figure below. If E1 = 42.4 N/C and E2 = 23.1 N/C, what is the net flux through the two end faces of the cylinder? Note that the diagram is not to scale.arrow_forwardConsider the uniform electric field E → = (4.0 j ^ + 3.0k ^ ) × 103 N/C. What is its electric flux through a circular area of radius 2.0 m that lies in the xy-plane?arrow_forward
- A particle with charge Q is located on the axis of a circle of radius R at a distance b from the plane of the circle (as shown). Show that if one-fourth of the electric flux from the charge passes through the circle, then R = √(3b).arrow_forwardA point charge Q is located on the axis of a disk of radius R at a distance h from the plane of the disk. Using Gauss' Law show that if one fourth of the electric flux from the charge passes through the disk, then R= V3harrow_forwardOne spherical gaussian surface is drawn on the inside of a hollow sphere with a charge of 6.0 µC. What is the net flux through the gaussian surface? Explain how you know this is the case.arrow_forward
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