Problem 3. Consider two thin coaxial cylindrical shells as in the figure, the inner one with radius Rin and the outer on

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Problem 3 Consider Two Thin Coaxial Cylindrical Shells As In The Figure The Inner One With Radius Rin And The Outer On 1 (115.04 KiB) Viewed 52 times

Problem 3 Consider Two Thin Coaxial Cylindrical Shells As In The Figure The Inner One With Radius Rin And The Outer On 2 (89.84 KiB) Viewed 52 times

Problem 3. Consider two thin coaxial cylindrical shells as in the figure, the inner one with radius Rin and the outer one with radius Rout, and both of much larger length L. Suppose that the inner cylindrical shell carries a total charge Q and the outer one a total charge - uniformly distributed on their surfaces. e for L a) Ignoring fringe effects, determine the magnitude E of the electric field as a function of the distance r from the central axis i) inside the inner cylindrical shell (0 <r < Rin) ii) between the cylindrical shells (Rin <r <Rout) iii) outside the outer cylindrical shell (Rout <r). (For full credit sketch in each case or describe in words the gaussian surface, and write down the corresponding form of Gauss's law used to determine E.) b) Plot on a single graph E as a function of r, across all three regions. (For full credit your sketch should be neat, and should include two tick marks along the r-axis at r = Rin and r= = Rout.) c) What are the maximum and minimum values of E in the region between the cylindrical shells?

Problem 4. Three identical positive point charges Q = 3.0 C are kept fixed in three corners of a square of side I=10 cm. 1 a) What is the net electric potential created by them in the remaining corner? Make the usual assumption that the electric potential of a charge tends to zero far away from it. b) What work must be done in order 9 = 2.0 C to the unoccupied corner? bring from infinitely far away a fourth positive point charge c) Suppose that, after being brought to that corner, the fourth point charge is released. Under the influence of the repellent electric forces exerted by the fixed charges this will then be thrust out. If its mass is m = 10g, what speed will it eventually reach very far away?