3.1 Introduction to Electric Flux
Electric flux is a measure of the electric field passing through a given surface. It helps us understand how the electric field interacts with objects and how charges distribute themselves on the surfaces of objects. In this chapter, we will discuss the concept of electric flux in more detail and introduce its applications.
3.2 Calculating Electric Flux
As introduced in the previous chapter, the electric flux (
) through a surface can be calculated as the dot product of the electric field vector (
) and the vector area (
) of the surface:
where 
is the angle between the electric field and the vector pointing normal to the surface.
3.3 Electric Flux through a General Surface
For general surfaces, we can calculate the net electric flux through the entire surface by integrating the electric field over that surface:
Here, the symbol 
represents the surface integral, which sums up the contributions of electric flux over the entire surface.
It should be noted here that this equation is generally not all that useful. However, in the next chapter, it will take a much more powerful form.
3.4 Applications
One primary application of electric flux is Gauss’s Law, which relates the net electric flux through a closed surface to the total charge enclosed by the surface. Gauss’s Law will be discussed in more detail in Chapter 4.
Another application of electric flux is calculating the electric field due to complex charge distributions. By exploiting the symmetry of certain charge distributions, one can use electric flux calculations to determine the electric field at various points in space. This will be discussed in greater detail when we talk about Gauss’ Law in the next chapter.
Chapter Summary
In this chapter, we have discussed the concept of electric flux in greater detail, exploring its calculation and applications. We have also covered the behavior of electric flux in the context of conductors. Understanding electric flux is essential for grasping more advanced topics in electricity and magnetism, such as Gauss’s Law and the behavior of electric fields in complex systems.
Continue to Chapter 4: Gauss’ Law
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