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

Question

An electric field due to an infinite line of charge is perpendicular to the line and has magnitude E=?/2??0r. Consider an imaginary cylinder with a radius of r = 0.190m and a length of l = 0.425m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is ? = 4.35?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= 0.530m?

C

What is the flux through the cylinder if its length is increased to l= 0.880m?

Explanation / Answer

1.
Flux = q/eo = lambda * L/eo
Flux = 4.35 x 10^-6 * 0.425 / 8.85 x 10^-12
Flux = 2.1 x 10^5 Wb

(b)
Flux will be same as it does not depend on radius

(c)
Flux = 4.35 x 10^-6 * 0.880 / 8.85 x 10^-12
Flux = 4.325 x 10^5 Wb

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