A point charge q is placed at origin. Find the flux of electric,produced due to this charge, through a circle of radius R lying in y-z plane. The centre of the circle lies at (x,0).

Explanation

The circular surface can be supposed to made up of rings. Consider one such ring of radius r and thickness dr.
The flux of electric field through the ring is given by
`dphi = vec(E). vec(dA)`
`=E. ( 2pi r dr) cos theta [:' dA =2pirdr]`
`implies d phi = (q)/( 4pi epsilon_(0)(x^(2)+r^(2)))(2pi r dr ) cos theta`
`implies d phi = ( qx)/( 2epsilon ) xx int_(0)^(R ) ((r dr)/((r^(2) + x^(2))^(2)) [ :' cos theta = ( x)/( sqrt(r^(2)+x^(2)))]`
Taking `r^(2) + x^(2) = t^(2)`
We have `r dr = tdt`
Ar ` r= 0 , t = x`