An polaroid long cylindrical object with radius R has a charge distribution that depends upon distance r from the axis like this : `rho = ar + br^(2)(r le R`, a and b are non zero constant, `rho` is volume charge density). If electric field outside the cylinder is zero than value of `(a)/(b)` is :

Options

A. `3R//4`
B. `-3R//4`
C. `-4R//3`
D. `4 R//3`

Answer

B

Explanation

By Gauss Theoren
Net charge inside cylinder =0
`rArr int (2 pi r dr)h rho=0 rArr underset(O)overset(R)(int) (ar+br^(2))rdr =0`
`rArr (aR^(3))/(3)+(bR^(4))/(4) =0rArr (a)/(b) =-(3R)/(4)`