The figure shows two identical long straight metal wires, A and B placed parallel to z-axis the cross sectional radius of each wire is R and the separation of the two wires is `Dgt gtR`. The electric potential at a perpendicular distance `rgtR` from a long straight wire due to that wire is given by `V=-kln((r)/(R))` where `k` is a positive constant. the wires carry charges `+Q` and `-Q` per unit length respectively. Then
Q. As `D gt gt R`, the electric field due to a long straight wire has cylindrical symmetry. The charge per unit length of the wire is

Options

A. `kepsi_(0)`
B. `pikepsi_(0)`
C. `4pikepsi_(0)`
D. `2pikepsi_(0)`

Answer

C

Explanation

`E=(-dV)/(dr)=(k)/(r)`
comparing with `E=(lamda)/(2piepsilon_(0)r)`
`lamda=2piepsilon_(0)k`