If the charge density of a non-uniform spherical charge distribution varies as ρ(r) = kr², what is the electric field at the center of the sphere?
Practice Questions
1 question
Q1
If the charge density of a non-uniform spherical charge distribution varies as ρ(r) = kr², what is the electric field at the center of the sphere?
0
k/3ε₀
k/4ε₀
k/2ε₀
At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.
Questions & Step-by-step Solutions
1 item
Q
Q: If the charge density of a non-uniform spherical charge distribution varies as ρ(r) = kr², what is the electric field at the center of the sphere?
Solution: At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.
Steps: 4
Step 1: Understand that we have a spherical charge distribution where the charge density varies with the distance from the center, given by ρ(r) = kr².
Step 2: Recognize that the center of a sphere is a point where all directions are symmetrical.
Step 3: Recall that electric fields from symmetrical charge distributions cancel each other out at the center.
Step 4: Conclude that because of this symmetry, the electric field at the center of the sphere is zero.
