# Does Gauss' Law Hold for Non-Conservative Electric Fields?

• miss photon
In summary, the electric field produced by a time varying magnetic field is non-conservative, meaning it cannot be fully determined by Gauss's law. Gauss's law only defines the conservative component of the electric field, while Faraday's law defines the non-conservative component. This means that the induced electric field cannot be determined by Gauss's law alone, but it also does not violate Gauss's law. To fully describe the electric field, all four of Maxwell's equations are needed. While all electric fields do satisfy Gauss's law, it is not enough to determine the fields in all cases as it must be supplemented by an equation giving the curl.
miss photon
the electric field produced due to a time varying magnetic field is non-conservative in nature. does it follow gauss law?

Gauss law does not completely define electric field: it only defines the conservative component. Similary Faraday's law defines the non-conservative component, that gives 0 when integrated over suface of any volume.
So induced electric field is can't be determined by Gauss law, but does not violate Gauss law, because it contributes 0 to both sides od the equation.

another way to think about it is that if the charge enclosed in the closed surface referred to by Gauss's Law were constant, then we know that Gauss's Law is accurate and there is no net current that crosses the surface boundary. but there can be a current flowing in that is equal to the current flowing out. if that current is not time variant, then Gauss's Law still works, but if the current flowing into the closed surface remains equal to the current flowing out but they're varying in time, then Gauss's Law needs Faraday's Law to fully describe what's going on. really you need all four of Maxwell's Eqs. to fully describe what's going on.

miss photon said:
the electric field produced due to a time varying magnetic field is non-conservative in nature. does it follow gauss law?
All electric fields satisfy Gauss's law.

pam said:
All electric fields satisfy Gauss's law.

True. :)

But Gauss's law only gives the divergence... it must be supplemented by an equation giving the curl. So, although all electric fields satisfy Gauss's law, Gauss's law is not enough to determine the fields in all cases.

miss photon said:
the electric field produced due to a time varying magnetic field is non-conservative in nature. does it follow gauss law?
Yes....

## 1. What is Gauss' Law?

Gauss' Law is a fundamental law in physics that relates the electric flux through a closed surface to the total charge enclosed within that surface. It states that the electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space. This law is a consequence of the fact that electric fields originate from electric charges.

## 2. Does Gauss' Law apply to non-conservative electric fields?

Yes, Gauss' Law applies to both conservative and non-conservative electric fields. It is a general law that holds true in all cases.

## 3. Can you provide an example of a non-conservative electric field?

One example of a non-conservative electric field is an electric field created by a changing magnetic field. In this case, the electric field is not a conservative field because the work done by the electric field on a charged particle depends on the path taken by the particle.

## 4. How is Gauss' Law used to calculate the electric field in a non-conservative field?

In order to use Gauss' Law to calculate the electric field in a non-conservative field, we need to know the total charge enclosed within a closed surface and the electric flux through that surface. The electric field can then be calculated by dividing the total charge by the permittivity of free space.

## 5. Why is Gauss' Law important in understanding the behavior of electric fields?

Gauss' Law is important because it is a fundamental law that helps us understand how electric fields are created and how they interact with charges. It also allows us to make predictions about the behavior of electric fields and to calculate their strength in different situations.

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