Gauss's law intuitive explanation?

In summary, Gauss's law states that the electric flux through any closed surface is proportional to the enclosed electric charge, and can be used to determine the electric field in a particular region by enclosing it with a Gaussian surface. It is a form of conservation of energy for a field and can be applied in many different contexts to understand the behavior of various fields.
  • #1
lord_james
1
0
I'm not sure what Gauss's law really means. "The electric flux through any closed surface is proportional to the enclosed electric charge." How does this apply to finding the electric field?
apcentral.collegeboard. com/apc/public/repository/ap11_frq_physics_cem.pdf
Look at parts 1 a and b. Part 1a is easy enough to do, but I want to really understand why Gauss's law applies here. collegeboard. com/apc/public/repository/ap11_physics_c_electricity_magnetism_scoring_guidelines.pdf
Here are their solutions. (Remove the space before com in both links). The fact that the enclosed charge is zero does not tell you anything about the electric field, though, as evidenced by part (b). What if I draw a Gaussian surface next to, but not enclosing, a point charge? There is no enclosed charge, and no net flux, but there is still obviously an electric field. So why do they want Gauss's law used in these situations?
 
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  • #2
lord_james said:
I'm not sure what Gauss's law really means. "The electric flux through any closed surface is proportional to the enclosed electric charge." How does this apply to finding the electric field?
apcentral.collegeboard. com/apc/public/repository/ap11_frq_physics_cem.pdf
Look at parts 1 a and b. Part 1a is easy enough to do, but I want to really understand why Gauss's law applies here. collegeboard. com/apc/public/repository/ap11_physics_c_electricity_magnetism_scoring_guidelines.pdf
Here are their solutions. (Remove the space before com in both links). The fact that the enclosed charge is zero does not tell you anything about the electric field, though, as evidenced by part (b). What if I draw a Gaussian surface next to, but not enclosing, a point charge? There is no enclosed charge, and no net flux, but there is still obviously an electric field. So why do they want Gauss's law used in these situations?

Gauss' Law in it's mathematical form is [tex] \oint\vec E \cdot \vec {da} = \dfrac{1}{\epsilon _o}Q_{enc}[/tex]. If we draw a Gaussian surface encompassing the region in which we seek to determine the electric field, the left side of the equation 'picks out' the all sources in this region, and says that the electric field is proportional to the charge enclosed only in this region we've defined with our Gaussian surface, which is the right side of the equation. Notice that in regions that no charge is enclosed, the left side of the equation is zero because all flux entering a Gaussian surface leaves the surface as well.
 
  • #3
In reference to your statement about the enclosed charge equaling zero telling you nothing about the [itex]\vec E [/itex] field, that's false. It tells you that [itex]\vec E = 0[/itex]. Gauss' Law allows you to determine electric fields for regions. If you want to know the field in a particular region, the Gaussian surface must enclose that region, and the charge generating the field.
 
  • #4
lord_james said:
I'm not sure what Gauss's law really means. <snip>

Gauss's law is a form of conservation of energy for a field. For example, we say that a charge generates an electric field. If you enclose the charge with a spherical surface, the electric field at the surface is Q/r^2. No matter what radius you choose, the total field 4πr^2*Q/r^2 through the surface is constant.

Conceptually, Gauss's law in electrostatics states that electric charges create electric fields, magnetic charges create magnetic fields (and since there are no magnetic charges, div(B) = 0). Gauss's law (in other contexts) means the intensity of light from a point source falls off quadratically with distance, the gravitational field of a point source falls off quadratically with distance, etc. etc.
 
  • #5


Gauss's law is a fundamental principle in electromagnetism that relates the electric field to the distribution of electric charge. It states that the electric flux through any closed surface is proportional to the enclosed electric charge.

Intuitively, this means that the electric field is created by the presence of electric charges. The more charges there are, the stronger the electric field will be. This is similar to how a magnet creates a magnetic field - the more magnets you have, the stronger the magnetic field will be.

In terms of finding the electric field, Gauss's law allows us to use a mathematical tool called a Gaussian surface to simplify the calculation. A Gaussian surface is an imaginary surface that we can draw around a charge or a group of charges. By using Gauss's law, we can calculate the electric flux through this surface and relate it to the enclosed charge. This allows us to find the electric field at any point outside the surface without having to consider the individual contributions of each charge.

In the context of the AP Physics C exam, Gauss's law is often used to calculate the electric field due to a continuous charge distribution. In part 1a of the released exam, the enclosed charge is a point charge, so it is easy to use Coulomb's law to find the electric field. However, in part 1b, the enclosed charge is a charged rod, which is a continuous distribution of charge. Using Gauss's law allows us to simplify the calculation and find the electric field at a point outside the rod.

In the scoring guidelines for part 1b, the enclosed charge is indeed zero, but this does not mean that there is no electric field. As you mentioned, if we draw a Gaussian surface next to, but not enclosing, a point charge, there is still an electric field. This is because the electric field is a vector quantity and can exist even when there is no net charge. However, in the case of a continuous charge distribution, Gauss's law allows us to find the electric field at a point outside the distribution by considering the net charge enclosed by the Gaussian surface.

Overall, Gauss's law is a powerful tool that helps us understand and calculate the electric field in different scenarios. It is an essential concept in electromagnetism and plays a crucial role in solving problems related to electric charges and fields.
 

What is Gauss's law?

Gauss's law is a fundamental law of electromagnetism that describes the relationship between electric charges and the electric field they create. It states that the total electric flux through a closed surface is equal to the enclosed electric charge.

How does Gauss's law work?

Gauss's law is based on the concept of electric flux, which is the measure of how much electric field passes through a given area. When a charge is enclosed by a closed surface, the electric flux through that surface is directly proportional to the enclosed charge.

What is the intuitive explanation of Gauss's law?

The intuitive explanation of Gauss's law is that it shows how electric charges create an electric field that spreads out in all directions. The strength of the electric field is directly proportional to the amount of charge enclosed by a given surface.

What is the significance of Gauss's law?

Gauss's law is significant because it allows us to calculate the electric field at any point in space, as long as we know the distribution of electric charges. It is also important in understanding the behavior of electric fields, such as how they interact with conductors and insulators.

How is Gauss's law used in practical applications?

Gauss's law is used in various practical applications, such as in designing electrical circuits, calculating the capacitance of a capacitor, and understanding the behavior of lightning. It is also used in the study of electromagnetic fields and their effects on different materials.

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