Top view of a Gaussian surface in a uniform electric field

In summary, the electric flux through a surface with area A and a uniform electric field is given by \Phi_E = EA\cos\theta . This is represented as a dot product between the electric field vector and the area vector, and the angle between them is θ. This formula is used to find the electric flux through each face of a surface, with the exception of the top and bottom faces where the flux is always 0. The use of cosine or sine depends on the angle between the electric field vector and the area vector, with cosine being used when the angle is 0 and sine being used when the angle is 90 degrees.
  • #1
brojas7
20
0
The field makes an angle θ with side 1 and the area of each face is A. In symbolic form, find the electric flux through (a) face 1, (b) face 2, (c) face 3, (d) face 4 and (e) top and bottom.

My professor got:
a=EAcosθ
b=-EAsinθ
c=-EAcosθ
d=EAsinθ
e= 0
I understant why e=0 but for the other sides, for some reason I am not understanding why she got for example a=EAcosθ and not sinθ. Which part of the triangle am I trying to find out? Would it be the adjacent for each or the opposite side for each?

I hope my question makes sense.

gaussiansurface_zps89f0cc05.jpg

 
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  • #2
brojas7 said:
The field makes an angle θ with side 1 and the area of each face is A. In symbolic form, find the electric flux through (a) face 1, (b) face 2, (c) face 3, (d) face 4 and (e) top and bottom.

My professor got:
a=EAcosθ
b=-EAsinθ
c=-EAcosθ
d=EAsinθ
e= 0
I understant why e=0 but for the other sides, for some reason I am not understanding why she got for example a=EAcosθ and not sinθ. Which part of the triangle am I trying to find out? Would it be the adjacent for each or the opposite side for each?

I hope my question makes sense.

gaussiansurface_zps89f0cc05.jpg
For a uniform electric field, and a flat surface, the electric flux [itex] \Phi_E [/itex] through a surface with area A is

[tex] \Phi_E = \vec E \cdot \vec A [/tex]

Notice I'm using vector notation. The direction of [itex] \vec A [/itex] is normal to the surface. And there's a loose convention that for a closed surface, the surface vector points out of the surface. (That's just a convention though, although that conversion is used here.)

Another thing to notice is that we're dealing with the "dot" product. Another way to represent the dot product is

[tex] \vec E \cdot \vec A = EA \cos \theta [/tex]

The dot product measures (in part) how parallel two vectors are. If they are perfectly parallel, the dot product is simply EA. If they are perpendicular the dot product is 0. If they are in perfectly opposite directions, the dot product is -EA.

If it helps, imagine the situation where [itex] \theta [/itex] is 0, and other situation where it is 90o. If [itex] \theta [/itex] is 0, a maximum amount of flux would pass through side 1. How many flux lines would pass though side 1 when [itex] \theta [/itex] is 90o? So would cosine or sine be used to represent that?
 
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1. What is a Gaussian surface in relation to an electric field?

A Gaussian surface is an imaginary surface that is used to calculate the electric field at a point. It is a closed surface that encloses a charge or charges and has a symmetrical shape, such as a sphere or cylinder.

2. How is the electric field calculated for a Gaussian surface?

The electric field at a point on a Gaussian surface is calculated by using Gauss's law, which 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.

3. What is the significance of using a Gaussian surface in a uniform electric field?

In a uniform electric field, the electric field strength is constant at all points. By using a Gaussian surface, which has a symmetrical shape, the calculation of the electric field at a point becomes simpler as the electric field is constant over the surface and can be easily integrated.

4. How is a Gaussian surface represented in diagrams?

A Gaussian surface is often represented by a dashed line or a dotted line in diagrams. It is also labeled with a letter, such as "S," to indicate which surface is being used for the calculation.

5. Can a Gaussian surface be used for non-uniform electric fields?

Yes, a Gaussian surface can be used for non-uniform electric fields as long as the electric field is constant over the surface. However, in non-uniform fields, the calculation of the electric field at a point becomes more complex and may require more advanced mathematical techniques.

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