Let `p=(Qr^(3))/(piR^(5))` be the volume charge density at distance r from the centre for a a soild sphere of radius R and charge Q. The electric field at `r= (R)/(2)` from the centre will be

Options

A. `(Q)/(4piepsi_(0) R^(2))`
B. `(Q)/(40piepsi_(0) R^(2))`
C. `(Q)/(8piepsi_(0) R^(2))`
D. None

Answer

2

Explanation

`oint vecE.dvecs =(q_("sin"))/(epsi_(0))`
`E. 4 pr ^(2)=(q_("in"))/( epsi_(0))`

`E =( q_("in"))/(4 pi epsi_(0)r^(2))" ".......(i)`
where `q_("in") = underset(0) overset(r)int rho4pi r^(2) dr`
`= underset(0)overset(r)int (Qr^(2))/(piR^(5)) 4pir^(2) dr`
`=(4Q)/(R^(5)) (r^(5))/(5)`
`therefore `from (1)
`E =(1)/(4piepsi_(0)r^(2))xx (4)/(5) (Qr^(5))/(R^(5))`
`E=(Q)/(5piepsi_(0))(r^(3))/(R^(5))`
at `r =(R)/(2) =, E =(Q)/(5piepsi_(0)R^(5))((R)/(2))^(3)`
`E=(Q)/(40epsi_(0)R^(2))`