Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 5.3, Problem 1bT
In the following Questions, a Gaussian cylinder with radius a andl is placed in various electric fields. The end caps are labeled A and C and the side surfaces is labeled B. In each case, base your answer about the net flux only on qualitative arguments about the magnitude of the flux through the end caps and side surfaces.
B. The Gaussian cylinder encloses a negative charge. (The field from part A is removed.)
• find the sign of the flux through:
Surface A: Surface B: Surface C:
• Is the net flux through the Gaussian surface positive, negative, or zero?
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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.
Consider a right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is numerically equal to 94 meters, and AC is thrice AB, find the magnitudes of the force and of the electric field at B.
Consider a very thin semi-circle of charge as shown, with radius of R. Explain with words and equations how you would derive the electric field vector measured at the center of this line of charge curved into a semi-circle with radius R (Measure E at the origin).
Chapter 5 Solutions
Tutorials in Introductory Physics
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