A long cylinder (radius = 3.0 cm)is filled with a nonconducting material which carries a uniform charge density of 1.3 $\mu$C/m³.Determine the electric flux through a spherical surface (radius = 2.0 cm)which has a point on the axis of the cylinder as its center.

Question

Quizplus · Accepted Answer

The electric flux through the spherical surface is given by:
ϕ = Qenclosed/ε0
where Qenclosed is the charge enclosed within the spherical surface and ε0 is the permittivity of free space.

Since the cylinder has a uniform charge density, the total charge enclosed by the spherical surface can be calculated as:
Qenclosed = ρV
where ρ is the charge density, and V is the volume enclosed by the spherical surface.

The volume of the cylinder enclosed by the spherical surface can be calculated as:
V = πh(r^2 - h^2/3)
where h is the distance between the center of the sphere and the plane of the ends of the cylinder, r is the radius of the cylinder. In this case, h = 3 cm and r = 3 cm.

Substituting the values, we get:
V = π(3 cm)(3^2 cm^2 - (3 cm)^2/3) = 54π cm^3

The charge enclosed within the spherical surface is:
Qenclosed = (1.3 μC/m^3)(54π cm^3) = 69.66 μC

Substituting back into the expression for electric flux, we get:
ϕ = (69.66 μC)/(8.85 x 10^-12 C^2/N*m^2) = 4.9 x 10^11 N*m^2/C or 4.9 N*m^2/C

Therefore, the best choice is B.

A Long Cylinder (Radius = 3 μ\muμ C/m3

A Long Cylinder (Radius = 3 $\mu$ C/m³