Question

A cylindrical shell of radius 7.00cm and length 2.40m has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0cm radially outward from its axis (measured from the midpoint of the shell) is 36.0kN/C.

Find...
(a) the net charge on the shell, and...
(b) the electric field at a point 4.00cm from the axis, measured radially outward from the midpoint of the shell.

Answer 1

I need to set up a Gaussian surface, so I'll use Gauss' Law:
\[\oint \vec{E} \cdot d \vec{A}=\frac{q_{enc}}{\epsilon_0} \rightarrow q_{enc}=\epsilon_0\oint \vec{E} \cdot d \vec{A}\]I'm struggling upon what to choose as my Gaussian surface, though. I've talked to my professor and he basically said to use a cylinder with the same height as the original cylinder, just a larger radius because the surface areas of the endcaps of the cylinder don't affect the electric field.

I understand that since the cylinder is much much taller than wide that the electric field lines are going to be essentially horizontal radiating from the cylinder, but I'm just trying to wrap my head around using a cylindrical Gaussian surface.

Can anyone outline, or help me through the steps I need to take to solve this?

Answer 2

E 2 p r L = Q/e0
Q = E 2 p r L e0
Q = (36.0 kN/C) 2 p(0.190 m) (2.40 m) e0= 9.13 x 10-7C

Answer 3

@Xishem

have a look into this : http://faculty.clayton.edu/Portals/507/Imported/a-s.clayton.edu/krivosheev/Spring03.phys2212/Spring03.Phys2212.quiz2.SolutionWeb.htm

Answer 4

Oh, thank you! That little bit of work seemed to clear up most of my doubts about the problem. Thank you for the link!

Answer 5

No problem and sorry I was not able to help u

Answer 6

You helped me by doing the thing I was too lazy to do -- google it :P.