Answer :
To find the linear charge density we can find the electric due ti infinite linear charge distribution.
Given : distance $r= 2 \;cm= 2 \times 10^{-2}\;m$
Electric field $E= 9 \times 10^4\;N/c$
Electric field due to infinite line charge
$E= \large\frac{\lambda}{2 \pi \in_0 r}$
Multiply and divide by 2.
$E= \large\frac{2}{2} \times \frac{\lambda}{2 \pi \in_o r} =\frac{2 \lambda}{4 \pi \in_0 r}$
Substituting the values we get,
$9 \times 10^4 = \large\frac{ 2 \times 9 \times 10^9 \times \lambda}{2 \times 10^{-2}}$
$\lambda= 10^{-7} \;c/m$
Hence the linear change density is $10^{-7} \;C/m$