An infinity long uniform line charge distribution of charge per unit length `lambda` lies parallel to the y-axis in the `y-z` plane at `z=sqrt3/2` a(see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the `x-y` plane with its centre at the origin is `(lambdaL)/(nepsilon_0)` (`epsilon_0=` permittivity of free space), then the value of n is

Answer

6

Explanation

Suppose that an infinite, charged wire is placed parallel to a rectangular area. Then, number of field lines passing through the rectangular area (denoted by ADC in figure) is equal to number of field lines passing through portion ABC of cylindrical surface. Hence flux through both of them will be same. Let us redraw the figure from the point of view of an observer viewing from y-axis.
Consider a cylinder a cylindrical suface of length L , centre of the charged wier having a radius `r = sqrt((a)/(2))^(2) + ((asqrt(3))/(2))^(2))`. From the figure it is clear that the flux passing throught of the rectangular area is equal to `(1)/(6)` of the flux passing thorugh this cylindrical surface .
So , `phi = (1)/(6) , (Q_(eno))/(epsi_(0)) " "rArr " " (1)/(6),(lambda L)/(epsi_(0))" "therefore " n = 6`