The volume charge density in a spherical ball of radius R varies with distance r from the centre as (r)= ₀ [1- ( r R )^3 ] , where, ₀ is a constant. The radius at which the field would be maximum is

Step-by-step solution

Given, (r)= ₀ [1- ( r R )^3 ] So, effective charge at r is q(r)= (r) V = ₀ [1- ( r R )^3 ] 4 3 r^3 For maximum value of field, array rlrl & d q(r) d r & =0 & 4 3 ₀ [3 r^2 (1- r^3 R^3 )+r^3 (- 3 r^2 R^3 ) ] & =0 & & 3 r^2- 3 r^5 R^3 - 3 r^5 R^3 & =0 & r^3 & = R^3 2 r & = R 2^ 1 / 3 array