Each of the two long parallel threads carries a uniform charge `lambda` per unit length. The threads are separated by a distance `l`. Find the maximum magnitude of the electric firld strength in the symmetry plane of theis system located between the threads.

Explanation

The field at `P` due to the threads at `A` and `B` are both of magnitude `(lambda)/(2pi epsilon_(0) (x^(2) + l^(2)//4)^(1//2))` and directed along `AP` and `BP`. The resulatant is along `OP` with
`E = (2 lambda cos theta)/(2pi epsilon_(0) (pi^(2) + pi^(1//2))^(1//2)) = (lambda x)/(pi epsilon_(0)(x^(2) + l^(2)//4))`
`= (lambda)/(pi epsilon_(0) [x + (l^(2))/(4x) - 2. (1)/(2 sqrt(x)) . sqrt(x) + l])`
`= (lambda)/(4 epsilon_(0) [(sqrt(x) - (l)/(2 sqrt(x)))^(2) + l])`
This is maximum when `x = l//2`, and then `E = E_(max) = (lambda)/(pi epsilon_(0) l)`