the electric field due to an infinite line of charge is perpendicular to the lin

Question

the electric field due to an infinite line of charge is perpendicular to the line and has magnitude E=/20r. Consider an imaginary cylinder with a radius of r = 0.210 m and a length of l = 0.405 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is = 4.95 C/m

(A What is the electric flux through the cylinder due to this infinite line of charge?

B) What is the flux through the cylinder if its radius is increased to r= 0.600 m ?

C) What is the flux through the cylinder if its length is increased to l= 0.915 m

Explanation / Answer

we have E=/20r

Given = 4.95 C/m

r = 0.21m

l = 0.405 m

A)

flux phi = E * A

phi = (/20r) * (2r*l)

phi = * l / 0

it is independent of 'r'

phi = 4.95 * 10^-6 * 0.405 / (8.85 * 10^-12)

phi = 2.26 * 10^5 N-m^2/C

B) for r = 0.6m also

phi = 2.26 * 10^5 N-m^2/C

c)

for l = 0.915 m

phi = 4.95 * 10^-6 * 0.915 / (8.85 * 10^-12)

phi = 5.11 * 10^5 N-m^2/C

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