Question

Let there be a spherically symmetric charge distribution with charge density varying as `rho(r)=rho(5/4-r/R)` upto `r=R`, and `rho(r)=0` for `rgtR`, where r is the distance from the origin. The electric field at a distance r(rltR) from the origin is given by
A. `(rho_(0)r)/(4epsilon_(0)) ((5)/(4)-(r)/(R))`
B. `(4pi rho_(0)r)/(3 epsilon_(0)) ((5)/(3)-(r)/(R))`
C. `(rho_(0)r)/(4epsilon_(0)) ((5)/(3)-(r)/(R))`
D. `(4rho_(0)r)/(3epsilon_(0)) ((5)/(4)-(r)/(R))`

Answer 1

Correct Answer - C
`int vec(E). dvec(A) = (Sigmaq)/(epsilon_(0))`
`E (4pir^(2)) = (1)/(epsilon_(0)) int rho dV`
`Sigma q = int_(0)^(r) rho dV = int_(0)^(r) rho_(0) ((5)/(4)-(r)/(R)) 4pir^(2)dr`
`Sigma q = 4pi rho_(0) [(5)/(4)((r^(3))/(3))-(1)/(R)((r^(4))/(4))]`
`E (4pir^(2)) = (4pi rho_(0))/(epsilon_(0)) [(5)/(4)((r^(3))/(3))-(r^(4))/(4R)]`