A very long cylindrical plastic rod of radius $a=2.5 cm$ has electric charge per unit length  ${\text{λ=+6.0×10}}^{\text{-7}}\text{C/m}$ distributed uniformly throughout its volume. This rod is surrounded by a concentric cylindrical metal shell of inner radius ${\text{R}}_{\text{1}}\text{=7.5\hspace{0.17em}cm}$ and outer radius ${\text{R}}_2\text{=10\hspace{0.17em}cm}$, as shown. The metal shell is initially uncharged. (Take $\ln 3=1.0986$)