Answer :
The charge [tex]q_{enc}[/tex] enclosed by the cylinder is 5.31 × 10⁻⁶ C.
To determine the charge [tex]q_{enc}[/tex] that is enclosed by the cylinder with cross-sectional area A=2.00×10⁻² m², we need to use Gauss's Law.
This law states that the electric flux through any closed surface is proportional to the charge enclosed within the surface.
Let's assume that the cylinder is placed in a uniform electric field E.
Then, the electric flux through the cylinder is given by:
Φ = EA
where Φ is the electric flux, E is the electric field, and A is the area of the cylinder.
Now, according to Gauss's Law, the electric flux through the cylinder is also proportional to the charge enclosed within the cylinder, [tex]q_{enc}[/tex].
Therefore, we can write:
Φ = [tex]q_{enc}[/tex] / ε₀
where ε₀ is the electric constant (also known as the permittivity of free space).
Equating the two expressions for Φ, we get:
EA = [tex]q_{enc}[/tex] / ε₀
Solving for [tex]q_{enc}[/tex], we get:
[tex]q_{enc}[/tex] = EAε₀
Plugging in the given values, we get:
[tex]q_{enc}[/tex]= (E = 3.00 × 10⁴ N/C) × (A = 2.00 × 10⁻² m²) × (ε₀ = 8.85 × 10⁻¹² F/m)
[tex]q_{enc}[/tex] = 5.31 × 10⁻⁶ C
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