Electric Field of a Charged Sphere?

  • #1
ronk

Homework Statement


A sphere of radius R has total charge Q. The volume charge density (C/m^3) within the sphere is ρ = ρ_0 (1 - r/R).

This charge density decreases linearly from ρ_0 at the center to zero at the edge of sphere.

a. Show that ρ_0 = 3Q/πR^3.
b. Show that the electric field inside the sphere points radially outward with magnitude E = (Qr/4πε_0 R^3) (4 - 3 r/R).
c. Find the electric field outside the sphere (r > R).

Homework Equations


Volume of a Sphere: V = 4/3 πR^3.

The Attempt at a Solution


I knew that ρ = Q/V and could make this equal to our given value of ρ to find ρ_0, but I was unable to get rid of the 4 in the denominator to find ρ_0.
 

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,829
6,650
I knew that ρ = Q/V
This is incorrect. The sphere does not have uniform charge. You need to integrate the charge density to relate it to the total charge.
 

Related Threads on Electric Field of a Charged Sphere?

  • Last Post
Replies
5
Views
2K
Replies
12
Views
5K
Replies
7
Views
297
  • Last Post
Replies
3
Views
14K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
21
Views
12K
  • Last Post
Replies
10
Views
2K
Replies
4
Views
6K
  • Last Post
Replies
1
Views
1K
Top