A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a
uniform charge density of 1.3 uC/m². 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.
a. 5.7 N·m2/C
b. 4.9 Nm2/C
c. 6.4 Nm2/C
d. 7.2 N·m2/C
e. 15 N·m2/C

The correct option is B

Explanation:

from the question we are told that

    The radius of the cylinder is

      The uniform charge density is  

      The radius of the spherical surface  

Generally the flux through the spherical surface  is mathematically represented as

Where   is the permittivity of free space with a value of  

Q is the quantity of charge which is mathematically represented as

Where V is the volume of the sphere which is mathematically represented as

substituting values

So

So