A point charge `q` is placed at a distance `d` form the center of circular disc of radius `R`. Find electric flux through the disc due to that charge

Options

A. `(q)/(epsilon_(0))(1-(l)/(sqrt(R^(2)+l^(2))))`
B. `(q)/(2epsilon_(0))(1-(l)/(sqrt(R^(2)+l^(2))))`
C. `(q)/(2epsilon_(0))((1)/(2)-(l)/(sqrt(R^(2)+l^(2))))`
D. `(q)/(epsilon_(0))((1)/(2)-(l)/(sqrt(R^(2)+l^(2))))`

Answer

A

Explanation

`dA=2pir(dr)E=(1)/(4piepsilon_(0))(q)/(r^(2)+l^(2))=dphi=E(dA)costheta`
`=(1)/(4piepsilon_(0))(q)/((r^(2)+l^(2)))2pir(dx)(l)/(sqrt(r^(2)+l^(2)))`
`(ql)/(2epsilon_(0))(rdr)/((r^(2)+l^(2))^(3//2))phi =(ql)/(2epsilon_(0)int_(0)^(R))(r dr)/((r^(2)+l^(2))^(3//2))`
`rArr phi=(-ql)/(2epsilon_(0))[(1)/(sqrt(r^(2)+l^(2)))]_(r=0)^(r=R)`
`=(ql)/(2epsilon_(0))[(1)/(l)=(1)/(sqrt(R^(2)+l^(2)))]=(q)/(2epsilon_(0))[1-(l)/(sqrt(R^(2)+l^(2)))]`