- #1

- 1,270

- 0

I am very confused by this tough question. I hope some experts of Gauss's Law can help me out! Any help is greatly appreciated!

For part b (r>R), I picked a coaxial cylinder with a radius r>R and of lengt L as the Gaussian surface

E=(Q_enclosed)/(A)(epsilon_o)

E=(lambda)L+2(lambda)L/(A)(epsilon_o)

E=3(lambda)L/(2pi*r*L)(epsilon_o)

E=3(lambda)/(2pi*r)(epsilon_o) [direction: radially outward]

Is this the correct answer Note that the radius of the hollow cylinder "R" is not used in any part of my calculation...did I do something wrong?

For part a, I got the electric field strength for r<R as [lambda/(2pi*epsilon_o*r)], and when I try to substitute r=R into the answers from part a & b, the electric fields DON'T match at the boundary....which further lowers my confidence of being right. But which part did I do it wrong? I can't find my error...Does anyone know how to solve this problem?

By the way, how come they use the term LINEAR charge density for a 3-dimensional hollow cylinder? Say, for example, if a certain hollow cylinder has a linear charge density of 2 C/m, what does it actually mean? A cylinder is definitely NOT a line...

Thank you again!

**1) A long thin straight wire with linear charge ensity lambda runs down the centre of a thin hollow metal cylinder of radius R. The cylinder has a net linear charge density (2*lambda). Take lambda as positive. Find the electric field (strengh & direction)**

a) inside the cylinder (r<R)

b) outside the cylinder (r>R)a) inside the cylinder (r<R)

b) outside the cylinder (r>R)

For part b (r>R), I picked a coaxial cylinder with a radius r>R and of lengt L as the Gaussian surface

E=(Q_enclosed)/(A)(epsilon_o)

E=(lambda)L+2(lambda)L/(A)(epsilon_o)

E=3(lambda)L/(2pi*r*L)(epsilon_o)

E=3(lambda)/(2pi*r)(epsilon_o) [direction: radially outward]

Is this the correct answer Note that the radius of the hollow cylinder "R" is not used in any part of my calculation...did I do something wrong?

For part a, I got the electric field strength for r<R as [lambda/(2pi*epsilon_o*r)], and when I try to substitute r=R into the answers from part a & b, the electric fields DON'T match at the boundary....which further lowers my confidence of being right. But which part did I do it wrong? I can't find my error...Does anyone know how to solve this problem?

By the way, how come they use the term LINEAR charge density for a 3-dimensional hollow cylinder? Say, for example, if a certain hollow cylinder has a linear charge density of 2 C/m, what does it actually mean? A cylinder is definitely NOT a line...

Thank you again!

Last edited: