Question

Consider a cylinder centered on the origin that extends infinitely in the +y and -y direction with a constant charge density σ. Let a point P be a distance α away from the origin along the x-axis. (a) Calculate E at the point P using a Coulomb integral. (don't forget to indicate direction). (b) If P were at the origin, without doing a calculation, what would be the E-field?
σ=Q/A

Answer 1

easy to do with Gauss's law - how is a Coulomb integral different? You mean by calculating forces then dividing by charge?

Answer 2

I am trying to learn how to apply the law for a point inside a hollow cylinder with uniform charge density.

Answer 3

Yes, but are you talking about Hamiltonians?

Answer 4

i don't know, my math is not at that level yet, i am learning the concepts of surface integras. if you can help me with the formula to calculate the electric field from the cylinder surface at a point inside the cylinder i will be very grateful

Answer 5

if i have a flat surface x by y cm, i can calculate E at a point (xyz), but i'm stuck with the cylinder surface. from the outside you just treat it like a line at the center of the cylinder, but inside that doesn't work, or does it?

Answer 6

The easy way is to use Gauss's Law which says\[\int\limits_{surface}^{}E *dA=Q _{enclosed}/\epsilon _{0} \]where * represents a vector dot product

We create a cylindrical surface whose radius is the same as the distance from the axis of the charged cylinder out to the point where we want to know the E field value. then the angle between E and the area normal is 0, so that the integral becomes\[\int\limits_{surface}^{}EdA=E \int\limits_{surface}^{}dA=EA\]Now on the right-hand side, Qenclosed in the surface is \[Q _{enclosed}=\sigma A _{cylinder}=\sigma (2 \pi r _{cylinder}l _{cylinder})\]so\[E (2 \pi \alpha l _{cylinder})=\sigma(2 \pi r _{cylinder} l _{cylinder})\]\[E=\sigma r _{cylinder}/\alpha\]


at the center E=0 because there is no Q enclosed

Answer 7

watching the short videos at http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/gauss-law/ will help

Answer 8

thanks, i will work on that :>

Answer 9

Under Learning activities, look at Problem 1: The Electric Field of a Line of Charge

Answer 10

i will go through the whole thing

Answer 11

that short video will show you the two approaches - which might help