What is the magnitude of the net charge enclosed by surface?

In summary, the closed surface has dimensions a = b = 0.302m and c=0.604m, and is located as shown in the figure. The electric field throughout the region is nonuniform and defined by E⃗ = (α+βx2)ˆı where x is in meters,α=4N/C, andβ=4N/(C·m2). The question asks for the magnitude of the net charge enclosed by the surface, with the answer in units of C. The attempted solution involved using E= (4+4x^2) and distributing the Epsilon naught value, but this was incorrect. The direction of the electric field is unknown, and Gauss' Law
  • #1
YeetForTheOneTime
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Homework Statement


A closed surface with dimensions a = b = 0.302m and c=0.604m is located as in the figure.
The electric field throughout the region is nonuniform and defined by E⃗ = (α+βx2)ˆı where x is in meters,α=4N/C, andβ=4N/(C·m2).?
What is the magnitude of the net charge enclosed by the surface?
Answer in units of C.

Homework Equations

The Attempt at a Solution


I tried to use E= (4+4x^2) and distribute the Epsilon naught value but obviously that is completely wrong. I am struggling and would appreciate any help that can be offered!
 

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  • #2
YeetForTheOneTime said:

Homework Statement


A closed surface with dimensions a = b = 0.302m and c=0.604m is located as in the figure.
The electric field throughout the region is nonuniform and defined by E⃗ = (α+βx2)ˆı where x is in meters,α=4N/C, andβ=4N/(C·m2).?
What is the magnitude of the net charge enclosed by the surface?
Answer in units of C.

Homework Equations

The Attempt at a Solution


I tried to use E= (4+4x^2) and distribute the Epsilon naught value but obviously that is completely wrong. I am struggling and would appreciate any help that can be offered!
What is the direction of the electric field?
Do you know Gauss' Law?
 

1. What is the net charge enclosed by a surface?

The net charge enclosed by a surface refers to the total amount of electric charge contained within a specific surface. This can be calculated by summing up the individual charges of all particles within the surface, taking into account their respective magnitudes and directions.

2. How is the net charge enclosed by a surface determined?

The net charge enclosed by a surface is determined by using Gauss's Law, which states that the electric flux through a closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space. This can be mathematically represented as Φ = Q/ε₀.

3. Does the shape of the surface affect the net charge enclosed?

Yes, the shape of the surface does affect the net charge enclosed. According to Gauss's Law, the electric flux through a closed surface is directly proportional to the net charge enclosed. Therefore, a change in the shape of the surface will result in a change in the amount of charge enclosed.

4. What is the difference between net charge enclosed and net electric flux?

The net charge enclosed refers to the total amount of electric charge contained within a specific surface, while net electric flux refers to the total amount of electric field passing through a closed surface. The two are related by Gauss's Law, but they represent different quantities.

5. How is the net charge enclosed related to the electric field within a surface?

The net charge enclosed is directly related to the electric field within a surface. According to Gauss's Law, the electric flux through a closed surface is proportional to the net charge enclosed. This means that the amount of charge enclosed within a surface will determine the strength of the electric field passing through that surface.

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