A long cylindrical shell of radius R has a uniform surface charge density oo on its upper half and opposite charge -00 o

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A Long Cylindrical Shell Of Radius R Has A Uniform Surface Charge Density Oo On Its Upper Half And Opposite Charge 00 O 1 (236.89 KiB) Viewed 19 times

A long cylindrical shell of radius R has a uniform surface charge density oo on its upper half and opposite charge -00 on the lower half, as shown in the figure. у co R х -00 • Find the potential inside and outside the cylinder. Use the method of separation of variables applied to the Laplace equation. • Assume the general solution of Laplace's equation in cylindrical coordinates is known, V (8,0) = 40 + bo In s + [sk (ak cos kø + Bksin ko) +s* (C# cos kø + dx sin ko)] = k=1 • Specify the coefficients inherent to the method through the orthogonality relations of the respective functions, 27 > sen ko cos lo do = 0 27 =1 1 - cos ko cos lo do = Toki 2л sen ko sen lo do = = TOKI Justify the possible use of discontinuity conditions, + V1 = V2 ƏVi aV2 an an σ Eo