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.

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.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

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