A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ=Kra, where K and a are constants and r is the radial distance from its centre. If the electric field at r=R2 is 18 times that at r=R, the value of a is (answer upto two decimal places)
Given ρ=Kra
E(r=r2)=18E(r=R)
qenclosedR/24πϵ0(R/2)2=18Q4πϵ0(R)2
⟹32qenclosedR/2=Q ...(1)
qenclosed=∫ρdv=∫Kra4πr2dr
qenclosedR/2=∫R/20Kra4πr2dr=4Kπ(a+3)(R2)(a+3)
Q=qenclosedR=∫R0Kra4πr2dr=4Kπ(a+3)(R)(a+3)
QqenclosedR/2=2a+3
putting in equation (1),
2(a+3)=32
∴a=2