An infinitely long, straight cylinder of radius R has a uniform charge density r

Question

An infinitely long, straight cylinder of radius R has a uniform charge density rho throughout its volume. Using symmetry and Gauss's law, find the magnitude and direction of the electric field at a point inside the cylinder. Use a cylindrical coordinate system with the axis of the cylinder coinciding with the z-axis, as shown in the illustrations below. The radial r-coordinate of each point is the distance to the central axis of the cylinder, and the angular psi-direction at each point is perpendicular both to the z-direction and to the r-direction as shown. What is the magnitude of the electric field at some point inside the cylinder, at a distance r_i

Explanation / Answer

EA = Q/epsilon

take small element of length t

E = pi x ri2 x t x rho/(2 x pi x ri x t x epsilon)

E = ri x rho/(2 x epsilon)

where epsilon = 8.85 x 10-12

b) positive r- direction

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