• Support PF! Buy your school textbooks, materials and every day products Here!

Electric field at the center of a hemisphere

  • #1
1
0

Homework Statement



What is the electric field at the center of a hemisphere bounded by r=a, 0<θ<pi/2 / and 0<∅< 2pi with a uniform surface charge density?

Homework Equations


(1/4piε0) p(r') ((r-r')/[r-r']^3) dr'

The Attempt at a Solution


Forgive my formatting
ds= (r^2)sinθdθd∅ (In direction of r)
p(r')=constant = σ
r=r (in the direction of r)
r'= 0 (I have trouble with understanding r and r')

E= (σ/4piε0) ∫(0 to 2pi) ∫(0 to /2pi) (r^3)sinθdθd∅ / (r^3)
E= (σ/4piε0) (2pi)(1)
E= (σ/2ε0)

Everywhere I look I see the answer to this problem is (σ/4ε0) and I cannot figure out where I am going wrong. I feel as though I am missing to include something in my equation but I am stumped, help would be appreciated.
 

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
2019 Award
13,341
3,151
I think you are missing the fact that ##\vec E## is a vector-- it has components (some of which are zero in your exercise)
 

Related Threads on Electric field at the center of a hemisphere

Replies
2
Views
3K
Replies
4
Views
10K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
9K
  • Last Post
Replies
8
Views
15K
Replies
2
Views
23K
Replies
4
Views
2K
Replies
5
Views
2K
Replies
3
Views
20K
Replies
2
Views
1K
Top