Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Question
Chapter 19.3, Problem 1bTH
(a)
To determine
Whether the flux
(b)
To determine
The comparison of the flux
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Part A through part D, please
Charge is distibuted uniformly over each of two spherical volumes with radius R. One sphere of charge is centered at the origin and the other at x=2R (Figure 1). Let left-hand sphere have positive charge Q and let the right-hand sphere have negative charge -Q .
Part A Find the magnitude of the net electric field due to these two distributions of charge at the point x=0 on the x-axis. Express your answer in terms of the variables Q , R , and appropriate constants.
Part B Find the magnitude of the net electric field at the point x=R/2 on the x-axis. Express your answer in terms of the variables Q , R , and appropriate constants.
Part C Find the magnitude of the net electric field at the point x=R on the x-axis. Express your answer in terms of the variables Q, R , and appropriate constants.
Part D Find the magnitude of the net electric field at the point x=3Ron the x-axis. Express your answer in terms of the variables Q, R, and appropriate constants.
You have a very (infinitely) long solid conducting cylinder with length L, base radius R, and total charge +Q.
(a) Use Gauss’s law to find the electric field vector inside and outside the cylinder. Explain your reasoning. You can give a verbal description of the electric field vector direction.
(b) Similar to how we found the electric field outside a conducting sphere to look like that of a point particle, what does the electric field outside the cylinder look like?
(c) Would the electric field inside the cylinder stay the same if the cylinder was instead insulating and uniformly charged? Explain why or why not?
In the configuration shown in the picture below, what is the total predicted angle for electric field at point a?
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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- Problem 2: A closed hollow cylinder (i.e., with capped ends) is situated in an electric field given by E(u) = E0(u5i + 7j + 22k). The cylinder’s axis is on the x-axis with its center at the origin. The cylinder’s height is L and its radius is R. Here u = x/x0 is a dimensionless variable, where x0 sets the scale of the field. Refer to the figure. Part (a) Integrate to find an expression for the total electric flux through the cylinder in terms of defined quantities and enter the expression. Part (b) For L = 8.7 m, R = 0.25 m, E0 = 4.5 V/m, and x0 = 1 m, find the value of the electric flux, in units of volt•meter, through the cylinder. Part (c) If the electric field is E(u) = E0(323u2i + 42j + 415k), enter an expression for the total flux in terms of defined quantities.arrow_forwardc. i. Compare the electric flux in a cubical surface of a side 10cm and spherical surface ofradius 10 cm, when a charge of 5µC is enclosed by them.ii. How does the electric field enclosing a given charge vary when the area enclosed bythe charged is doubled. Assuming the electric flux is constant.arrow_forwardPart 1 In Fig-1, there are two infinite planes A and B, parallel to YZ plane. Their surface charge densities are σA=34nC/m2 and σB=29nC/m2. The separation between the planes A and B is d=8m. Calculate the net electric field due to both the planes in unit vector notation in three regions shown in the Fig-1. a) (i) Find the electric field in unit vector notation in region I. x component of the electric field Give your answer to at least three significance digits.y component of the electric field Give your answer to at least three significance digits. (ii) Find the electric field in unit vector notation in region II. x component of the electric field Give your answer to at least three significance digits.y component of the electric field Give your answer to at least three significance digits. (iii) Find the electric field in unit vector notation in region III. x component of the electric field Give your answer to at least three significance digits. y component of the electric field Give…arrow_forward
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