Electric Field from Gauss' Law - Vector Form

In summary, Gauss' Law can be used to find the electric field due to a given charge distribution, but it is limited to cases of symmetry. The law relates the total enclosed charge to the electric flux through a Gaussian surface, which can be converted to an integral equation. This can be used to solve for the electric field in cases such as a point charge in space or a spherically symmetric charge distribution. However, for more complex distributions without symmetry, the flux is not enough to uniquely define the electric field. Therefore, it is not always possible to find the electric field using Gauss' Law alone.
  • #1
roshan2004
140
0
Gauss' Law-Can't we find the Electric Field (In the vector form) from Gauss' Law? Because in most of the problems I have been doing like the case of a Charge in a solid sphere, I can find the Magnitude of Electric Field by Gauss' Law but not the Electric Field. Am I wrong here?
 
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  • #2
You can use Gauss' Law to find the electric field due to a given charge distribution. However, it is very limited because Gauss' Law only deals with the divergence of the electric field. If you convert this to an integral equation, then it relates the total enclosed charge to the electric flux through a Gaussian surface.

If we have a problem that we can capitalize on symmetry, then we can sometimes solve for the electric field. For example, given that we have a point charge in space, we can choose a spherical shell as our Gaussian surface. Then, we know by symmetry that the electric field vectors must be normal to the Gaussian surface. Thus, the flux through the surface at a given point is equal to the sign and magnitude of the electric field vector. From this we can derive the electric field due to a point source. Likewise, we can use this again for any spherically symmetric charge distribution (like a uniform charge density spread across a sphere's surface or volume).

But once we lose these symmetries, then the flux will not be enough to uniquely define the electric field.
 
  • #3
The electric field at a given point is found to be a zero. is it true to say that there are no charges in other point. justify the answer please with example.
 

1. What is Gauss' Law in relation to electric fields?

Gauss' Law states that the electric flux through a closed surface is directly proportional to the charge enclosed by that surface. In other words, the electric field lines passing through a closed surface are proportional to the amount of charge inside that surface.

2. What is the vector form of Gauss' Law?

The vector form of Gauss' Law is expressed as ∮SE·dA = Qenc0, where ∮SE·dA represents the electric flux passing through a closed surface, Qenc is the enclosed charge, and ε0 is the permittivity of free space.

3. How is the direction of the electric field determined using Gauss' Law?

The direction of the electric field can be determined by considering the direction of the normal vectors to the closed surface. The electric field lines always point in the direction of the outward normal vectors, perpendicular to the surface.

4. Can Gauss' Law be used to calculate the electric field at any point?

Yes, Gauss' Law can be used to calculate the electric field at any point as long as the charge distribution is symmetric and the closed surface chosen for the calculation is also symmetric. This allows for simplification and easier calculation of the electric field.

5. How is Gauss' Law used in practical applications?

Gauss' Law is used in many practical applications, such as in the design of capacitors, in determining the electric field inside a conductor, and in calculating the electric field due to point charges or infinite line charges. It is also used in the study of electrostatics and in understanding the behavior of electric fields in different scenarios.

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