If the charge density of a non-uniform spherical charge distribution varies as ρ

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What’s inside this PDF?

Question: 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?

Options:

0
k/3ε₀
k/4ε₀
k/2ε₀

Correct Answer: 0

Solution:

At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.

If the charge density of a non-uniform spherical charge distribution varies as ρ

Practice Questions

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.

If the charge density of a non-uniform spherical charge distribution varies as ρ

What’s inside this PDF?

If the charge density of a non-uniform spherical charge distribution varies as ρ

Practice Questions

Questions & Step-by-Step Solutions

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