Answer:
[tex]Q= 7.566 \times 10 ^{-10} \, C[/tex]
Explanation:
Applying Gauss' Law to a cylindrical shell of radius 8 cm and height h, concentric to the charged shell, we get:
[tex]E(r) \cdot 2 \pi r h= \cfrac{\lambda h}{\epsilon_o}[/tex]
Where [tex]\lambda[/tex] is the charge per unit length, and so [tex]\lambda h = Q[/tex] is the charge inside the shell, and if we set [tex]h=2\, m[/tex] we can get the answer to our question.
Solving for [tex]Q[/tex] we get:
[tex]Q= \epsilon_o E(r) 2 \pi r h[/tex]
plugging in the values ( in SI units) we get:
[tex]Q= 7.566 \times 10 ^{-10} \, C[/tex]