Let there be a spherically symmetric charge distribution with charge density varying as `rho(r)=rho_(0)((5)/(4)-(r)/(R))` upto `r=R`, and `rho(r)=0` for `r gtR`, where r is the distance from the origin. The electric field at a distance `r(rlt R)` from the origin is given by

Options

A. `(4pi rho_0r)/(3epsilon_0)(5/3-r/R)`
B. `(rho_0r)/(4epsilon_0)(5/3-r/R)`
C. `(4rho_0r)/(3epsilon_0)(5/4-r/R)`
D. `(rho_0r)/(3epsilon_0)(5/4-r/R)`

Answer

B

Explanation

By Gauss’s law, the total charge up to distance r can be calculated as followed
`dq=4 pi r^2 dr. p_0 [5/4 -r/R] =4 pi p_0[5/4 r^2-r^3/R] dr implies q= int_0^r 4 pi p_0 [5/4 r^2 r^3/4R] dr`
As electric field intensity `E= (kq)/r^2 =1/(4 pi e_0) 1/r^2 .4 pi p_0 [5/4 (r^3/3)-r^4/(4R)] =(p_0r)/(4e_0) [5/3-r/R]`