Suppose the electric field in some region is found to be in spherical coordinates (k is some constant).
(a) Find the charge density ρ.
(b) Find the total charge contained in a sphere of radius R, centered at the origin. (Do it two different ways.)
Step 1 of 8</p>
Given, the electric field in spherical coordinates is where k is constant
Step 2 of 8</p>
To find the charge density of the sphere of radius ‘r’
The charge density is given by the equation,
From eq(1) = (
) = = ….(2)
Step 3 of 8</p>
Using Eq(2) we have,
= = ….(3)
Therefore, substituting Eq(3) in Eq(1)
Hence the charge density is given by,
Step 4 of 8 </p>
To find the total charge in the sphere of radius ‘R’ at the origin
First Method: Using Gauss’ law
The Gauss’ equation is given by
Where is the electric flux
Textbook: Introduction to Electrodynamics
Author: David J. Griffiths
The full step-by-step solution to problem: 9P from chapter: 2 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. The answer to “Suppose the electric field in some region is found to be in spherical coordinates (k is some constant).(a) Find the charge density ?.(b) Find the total charge contained in a sphere of radius R, centered at the origin. (Do it two different ways.)” is broken down into a number of easy to follow steps, and 43 words. Since the solution to 9P from 2 chapter was answered, more than 239 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Charge, some, Find, found, coordinates. This expansive textbook survival guide covers 12 chapters, and 550 solutions. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562.