Gauss' Law for a Nonuniform Field

In summary, the conversation discusses a closed rectangular surface with dimensions a = b and c, where the faces perpendicular to the field are a*b. The electric field throughout the region is nonuniform and given by E = 3*x xhat N/C. The flux is defined as the integral of E(dot)dA = qenclosed/Epsilon0, and it is possible to have a nonzero net flux if there is charge enclosed in the box.
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Redfire66
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Homework Statement


A closed rectangular surface with dimensions a = b and c where the faces perpendicular to the field are a*b. The left edge of the closed surface is located at position x = a, for c > a.The electric field throughout the region is nonuniform and given by E = 3*x xhat N/C,

Homework Equations


Flux = Integral of E(dot)dA = qenclosed/Epsilon0

The Attempt at a Solution


I'm just wondering about how this works, if there is no enclosed charge, then there shouldn't be a net flux.

I'm pretty sure the flux at one end is greater as it reaches the x = c face than at x = a, is it possible to have a nonzero net flux?
 
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Conclusion: there is charge in the box.
 
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FAQ: Gauss' Law for a Nonuniform Field

What is Gauss' Law for a Nonuniform Field?

Gauss' Law for a Nonuniform Field is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed within that surface and the electric field at each point on the surface. It is a generalization of Gauss' Law for a Uniform Field, which applies to situations where the electric field is constant throughout the surface.

How is Gauss' Law for a Nonuniform Field different from Gauss' Law for a Uniform Field?

As mentioned before, Gauss' Law for a Nonuniform Field is a generalization of Gauss' Law for a Uniform Field. This means that it applies to situations where the electric field is not constant throughout the surface, while Gauss' Law for a Uniform Field only applies to situations where the electric field is constant. Additionally, Gauss' Law for a Nonuniform Field takes into account the variation of the electric field at each point on the surface, while Gauss' Law for a Uniform Field only considers the overall electric field at the surface.

What is the mathematical expression for Gauss' Law for a Nonuniform Field?

The mathematical expression for Gauss' Law for a Nonuniform Field is ∮SE·dA = Qenc/ε0, where ∮SE·dA represents the flux of the electric field E through a closed surface S, Qenc is the charge enclosed within the surface, and ε0 is the permittivity of free space.

How is Gauss' Law for a Nonuniform Field used in practical applications?

Gauss' Law for a Nonuniform Field is used in many practical applications, particularly in the design and analysis of electric circuits and devices. It allows engineers to calculate the electric field at any point in a nonuniform field by using the charge enclosed within a specific surface. This information is essential for designing and optimizing the performance of electronic devices.

What are some limitations of Gauss' Law for a Nonuniform Field?

One limitation of Gauss' Law for a Nonuniform Field is that it assumes that the electric field is continuous and differentiable throughout the surface. This may not always be the case in real-world situations, especially when dealing with sharp edges or irregularly shaped surfaces. Additionally, Gauss' Law for a Nonuniform Field only applies to static electric fields, and cannot be used to analyze dynamic or time-varying fields.

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