A ball of radius R carries a positive charge whose volume density depends only on the separation r from the ball’s center as ρ = ρ 0 (1 – r/R), where ρ 0 is a constant. Assuming the primitivities of the ball and the environment to be equal to unity, find:
(i) The magnitude of the electric field strength as a function of the distance r both inside and outside the ball;
(ii) The maximum intensity E max and the corresponding distance r m .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) E = 
for r < R, E = 
for r > R
(ii) E max = 
for r m = 
R.
Sol. (i) E at a point inside the ball (r < R):
Consider an elemental shell of radius x and thickness dx. Electric field due to this small element at a distance r from center:
dE = 
, where dq = ρ dV [dV = Volume of elemental shell]
∴ dq = ρ 0 
(4πx 2 dx)
∴ E net = 
= 
= 
Solving we get, E in = 
E outside the ball (r > R) →
E net = 
E net = 
E net = 
(ii) E will be maximum at inside point when 
∴ 
⇒ r = 
∴ E max = 
= 
= 
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