Practice with finding electric fields due to charge distributions a. A cylindric

Question

Practice with finding electric fields due to charge distributions a. A cylindrical shell of radius b and with area charge density rho_s is centered on the z-axis. The cylinder has length a and is located in z between 0 and a. Find the E-field produced on the z-axis at height h for h> a. b. Verify that for your resulting expression for the field in a. are the same units as for Example 4-4 and for the field from a point charge c. Directly by integration find the E-field produced on the axis (z-axis) of a linear line charge of charge density rho_1. The line charge is of length a located in z between 0 and a d. [no credit but also] Compare result to the result in part a. with b approaching 0.

Explanation / Answer

a, The cylindrical sheel is of radius 'b' and height 'a'.

So, total charge contained in the cylinder is Q=ps.(2*pi*b*a) C where ps is the charge density as given.

Since, the cylinder is centered about z axis, all the electric flux lines will be generated in 360o azimuth plane centered about the z axis. That means, electric field produced will be radially outward from the axis of the cylinder.

In the given question, the electric field at a point along z-axis at height h>a is told to calculate. That electric field will be zero as no field line will be present in that direction.

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