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.)

Solution 9P

Step 1 of 8</p>

Given, the electric field in spherical coordinates is where k is constant

(a)

Step 2 of 8</p>

To find the charge density of the sphere of radius ‘r’

The charge density is given by the equation,

….(1)

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,

….(4)

(b)

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

….(5)

Where is the electric flux