Reference.:Physics for Scientist and Engineers 6th Edition 4.- (10 points) A uni

Question

Reference.:Physics for Scientist and Engineers 6th Edition

4.- (10 points) A uniformly charged non-conducting solid infinite cylinder of radius R has its center at the origin and has a volume charge density p. (a) Find the electric field in a point within the cylinder a distance r from the center (b) Material is removed from the cylinder leaving a cylindrical cavity that has a radius b = R/2 and its center at x = b on the x axis (as shown in the figure). Calculate the electric field at point P as shown in the figure. Hint: Model the cylinder with-cavity as two uniform cylinders of radius R and b and of equal positive and negative charge densities respectively (a) (b)

Explanation / Answer

a) =q/Venclosed

q=r^2l

from the gauss law   E*2rl=.r^2l/0

                                              E=r/20

b) with cavity

electric field E*2*2(R-b)l=*4(R-b)^2*l/0

there fore E=(R-b)/0

here R=b/2

so electric field E=R/20

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