If the charge density of a non-uniform spherical charge distribution varies as ρ
Practice Questions
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
Questions & Step-by-Step Solutions
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?
Correct Answer: 0
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.
Electric Field in Charge Distributions – Understanding how electric fields behave in non-uniform charge distributions, particularly in spherical symmetry.
Gauss's Law – Application of Gauss's Law to determine electric fields in symmetric charge distributions.
Symmetry in Physics – Recognizing that due to symmetry, the electric field at the center of a uniformly charged sphere is zero.
