Question

Two point charges q and -q are separated by a distance 2a. Evaluate the flux of the electric field strength vector across a circle of radius R.

Answer 1

Correct Answer - `(q)/(epsilon_(0))[1 - (1)/(sqrt(1 + ( R//a)^(2)))]`
`dphi = 2Ecos theta 2piydy`
`= 2 1/(4piepsilon_0)q/(a^2+y^2) (a2piydy)/(a^2+y^2)^(1//2)`
`phi = int d phi = (qa)/epsilon_0 int_(0)^R (ydy)/(a^2+y^2)^(3//2)`
` = q/(epsilon_0) [1-1/(sqrt(1+(R//a)^2))]`.