a cavity of radius `R` is taken out from a uniformly charged solid sphere with charge density `rho` and radius `2R` as shown Consider four points 1,2,3,4 at following positions,
1-`(2R,0,0)`
2- `(R,0,0)` ltbr. 3- `(0,0,0)`
4- `(3R,0,0)`
`E_(1),E_(2),E_(3),E_(4)` represents magnitude of net electric field at 1,2,3,4 respectively then the correct option (s) are:

Options

A. `(E_(1))/(E_(2))=(E_(2))/(E_(3))`
B. `(E_(4))/(E_(2))=(4)/(3)`
C. `(E_(4))/(E_(1))=(3)/(4)`
D. `(E_(4))/(E_(2))=(3)/(4)`

Answer

A, B, C

Explanation

`E=(rhor)/(3epsilon_(0))` [for inside cavity points] &

`((rhoR^(3))/(3epsilon_(0)r^(2))` for out side cavity points)
`E_(1)=E_(2)=E_(3)=(rhoR)/(3epsilon_(0))`
`E_(4)=(rhoR)/(3epsilon_(0))-(rho(R)^(3))/(3epsilon_(0)(2R)^(2))`
`=(rhoR)/(3epsilon_(0))-(rhoR)/(3epsilon_(0)xx4)=(rhoR)/(4epsilon_(0))`