A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C, how much charge is distributed on a 2.0-m length of the charged cylindrical surface?

Respuesta :

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]

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