A system consists of a ball of radius R carrying a spherically symmetric charge and the surrounding space filled with a charge of volume density ρ = α/r, where α is a constant, r is the distance from the center of the ball. Find the ball’s charge for which the magnitude of the electric field strength vector is independent of r outside the ball. How high is this strength? The permittivity’s of the ball and the surrounding space are assumed to be equal to unity.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
q = 2παR 2 , E = 
Sol. To calculate the electric field due to the charged sphere and the space surrounding the sphere, a shell of radius x and thickness dx whose center is the center of the sphere is taken and electric field due to this shell and charged sphere at a distance r from O is obtained as given below
E = 
× 
+ 
[where , q = charge considered on the ball]
Where, first term is the field strength of spherical charge q and second integral term is the field strength of space surrounding the charged sphere.
E = 
× 
+ 
so, E = 
+ 
or, = 
+ 
or, = 
+ 
or, = 
+ 
+ 
so, E = 
+ 
– 
Now, for E to be independent of r, sum of the first and third terms must be zero.
so, 
– 
= 0
or, q = 2παR 2 So, resultant field, independent of r, is given as
E = 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems