(Solution) - An infinitely long cylindrical shell is coaxial -(2025 Original AI-Free Solution)

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An infinitely long cylindrical shell is coaxial with the y axis and has a radius of 15 cm. It carries a uniform surface charge density ? = 6 ?C/m2. A spherical shell of radius 25 cm is centered on the x axis at x = 50 cm and carries a uniform surface charge density ? = ?12 ?C/m2. Calculate the magnitude and direction of the electric field at
(a) The origin
(b) x = 20 cm, y = 10 cm; and
(c) x = 50 cm, y = 20 cm. (See Problem 42.)