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 = lambda/2 pi epsilon_0 r. Consider an imaginary cylinder with radius r = 0.170 m and length l = 0.390 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is lambda = 7.00 mu C/m. What is the electric flux through the cylinder due to this infinite line of charge? What is the flux through the cylinder if its radius is increased to r = 0.340 m? What is the flux through the cylinder if its length is increased to l = 0.780 m?

Explanation / Answer

(a) Put the formula -

= (/2r)(2r)

(the radius cancels out because the flux is independent of the radius of the cylinder)

This simplifies to:

= (/)

= (7e-6 C/m)(0.39 m)/(8.85e-12 F/m)

= 308475 Nm²/C

(b) Same answer as A because the flux is independent of the radius.

(c) Again, = (/)

= (7e-6 C/m)(0.78 m)/(8.85e-12 F/m)

= 616949 Nm²/C

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