Answer:
The correct option is B
Explanation:
from the question we are told that
The radius of the cylinder is [tex]r = 3.0 cm = \frac{3}{100} = 0.03 \ m[/tex]
The uniform charge density is [tex]\eta = 1.3 \mu C/m^2 = 1.3 *10^{-6} C/m^2[/tex]
The radius of the spherical surface [tex]r_s = 2.0 \ cm = \frac{2}{100} = 0.02 \ m[/tex]
Generally the flux through the spherical surface is mathematically represented as
[tex]\phi = \frac{Q}{\epsilon_o}[/tex]
Where [tex]\epsilon_o[/tex] is the permittivity of free space with a value of [tex]\epsilon_o = 8.85*10^{-12} F/m[/tex]
Q is the quantity of charge which is mathematically represented as
[tex]Q = \eta * V[/tex]
Where V is the volume of the sphere which is mathematically represented as
[tex]V = \frac{4}{3} \pi r_s^3[/tex]
substituting values
[tex]V = \frac{4}{3}* 3.142 * 0.02^3[/tex]
[tex]V = 3.351*10^{-5} \ m^3[/tex]
So
[tex]Q = 1.3 *10^{-6} * 3.351*10^{-5}[/tex]
[tex]Q = 4.3569 *10^{-11} \ C[/tex]
So
[tex]\phi = \frac{ 4.3569 *10^{-11}}{8.85*10^{-12}}[/tex]
[tex]\phi = 4.92 N\cdot m ^2 /C[/tex]
The electric flux through the spherical surface is [tex]\rm 4.92\; N m^2 /C[/tex]
Gauss Law is used to determine the flux passing from a surface due to a point charge.
According to the given data
Radius of Cylinder = r = 3cm = 0.03 m
Let [tex]\rho[/tex] be the uniform charge density
[tex]\rho = 1.3 \times 10^{-6}[/tex] C/[tex]m^2[/tex]
Radius of Spherical Surface = 0.02 m
The Electric flux from spherical surface is given by equation (1)
[tex]\rm \phi = \dfrac{Q}{\epsilon_o}....(1) \\Q = Net \; Charge \\\epsilon_o} = Permittivity\; of \; Free \; Space = 8.85 \times 10^{-12\; }F/m[/tex]
Also [tex]Q= \rho \times V....(2)[/tex]
[tex]V = Volume \; of \; Sphere[/tex]
[tex]V = 4/3 \times \pi \ r ^3[/tex]
where r = Radius of the sphere
V = (4/3) [tex]\times[/tex] (3.14 )
Also from Equation (2) Q = 1.3 [tex]\times[/tex] [tex]10^{-6}[/tex] [tex]\times 3.315\times 10^{-4}[/tex]
Q = 4.3569 [tex]\times 10^{-11}[/tex] C
So
[tex]\phi = 4.3569 \times 10^{-11}/ 8.85 \times 10^{-12} \\\phi = 4.92 \; Nm^2 /C[/tex]
The electric flux through the spherical surface is [tex]\rm 4.92\; N m^2 /C[/tex]
For more information refer to the link below
https://brainly.com/question/15168926
