Question

What is the sign of the flux through the right-end of the cylinder

(A) Positive
(B) Negative
(C) There is no flux through the right-end cap
(D) Can’t say

Answer 1

We can start by defining the quantity of electric flux and what causes electric flux. Then we can discuss the dependence of electric flux with charge. Electric flux can be well understood by using the gauss theorem.
Gauss theorem gives us the relationship between electric flux and electric charge ${\phi _E} = \dfrac{Q}{{{\varepsilon _0}}}$
Where $Q$ is the charge
${\varepsilon _0}$ is the permittivity of free space.

Complete Step By Step Answer:
Electric flux is the property of an electric field that can be defined as the number of electric field lines through a given surface. Electric flux is an important part in understanding the strength of electric fields at a distance. Electric field lines are considered to start from a positive charge and end in a negative charge.
The concept of electric flux is introduced by the Gauss theorem, which gives us the relation
${\phi _E} = \dfrac{Q}{{{\varepsilon _0}}}$
According to this law, the electric flux depends only on the charge enclosed by the gaussian surface. The Gaussian surface is an imaginary surface through which the flux of a vector field is calculated. This law also helps us conclude that the only dependence of flux is with area, electric field and charge. The electric field is from positive charge to negative which means that it is to the right side and from the given image we know that the area vector is towards the right side as well.
In conclusion, the right answer is option (A) Positive.

Note:
According to the Gauss theorem, we can see that electric flux is a quantity that depends on the magnitude of charge, electric field and area of the gaussian surface. It also states that the quantity of electric flux does not depend on the shape or size of the gaussian surface.