Answered: The volume charge density of a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

The volume charge density of a spherical charge distribution is given by rho(r) = rho₀e^−alpha(r),

where rho₀ and alpha are constants. What is the electric field produced by this charge distribution? (Enter the radial component of the electric field. Use the following as necessary: rho₀, alpha, r, and epsilon₀.)

Expert Solution

Step 1 - Introduction & Concept

Given

$ρ (r) = ρ_{o} e^{- αr}$

to find the electric field produced by charge distribution we use Gauss law which is given by

$\int \vec{E} . \vec{ds} = \frac{q}{ε_{o}}$

as the volume charge distribution is given so

$q = \int ρ (r) dV = \int ρ (r) \times 4 {πr}^{2} dr$

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