# Electric field distance problem

ok, here is the question, i need it by tomorrow:

find the electric field of a distance z from the center of a spherical surface of radius r, which carries a uniform charge density sigma. treat the case z<r(inside the sphere) as well as z>r(outside of the sphere)> Express your answer in terms of the total charge Q on the sphere. (suggestion: use the law of cosines to write ro in terms of r and theta. be sure to take the positive sq rt) (also keep in mind that in spherical coordinates, unit vectors have nonzero derivatives)

chroot
Staff Emeritus
Gold Member
1) Do not post the same question in multiple places.

2) Do not expect anyone to treat your problem as an emergency, because you procrastinated on starting it.

3) Do not expect us to do your homework for you. Show what you've done so far, show us where you're stuck, and then we'll help you.

- Warren

berkeman
Mentor
4) Why do so many emergency questions in these forums come from members with one post?

(no disrespect to the regular members who post their work and ask for hints...)

i drew a diagram

i found ro, which is sq rt (z^2 + r^2 - zrcos(theta))

i also have dl = dr r direction + r dtheta theta direction + r sin theta d phi phi direction

dE = sigma/4piE0 da/ro squared

i need someone to help me with the calculus.

anyone willing to help?

ok, i did what i can. i don't know what more you want me to show so you could help me. if you are unwilling or unable to help, just say so. im just asking for a response. is that asking for too much?

anyone knows how to integrate that thing?

btw, you are not allowed to use gauss's law

anyone at all?

lightgrav
Homework Helper
Sorry nobody wanted to help ... or remembered how to do this (?).
1) you forgot the "2" in the law of cosines. you'll NEED it ...
2) Integrating around phi you'll get 2 pi ... and only the E_z will be non-zero.
3) dE_z = dE cos(alpha) ... get a formula for cos(alpha) from law of cosines.
4) Integrating theta from 0 to pi has this nasty denominator (& in alpha)
re-write the entire thing in terms of ro, so the denominator is clean.
Yes, the numerator is messy, but that's at least do-able. not so bad.
5) Integrate ro from z-R to z+R.

Give it a try ... the most important thing with E-fields is the distance
from source point to Field point ; secondary importance is dQ at that distance. Object orientation ... who cares?
Good Luck.