Flux - simple integral computation

In summary, the problem involves finding the flux of a uniform electric field through a surface with a given area vector. By taking the dot product of the electric field and the area vector, the flux can be determined.
  • #1
quantum13
66
0

Homework Statement


A surface has the area vector A = 2i + 3j. What is the flux of a uniform electric field through it if the field is E = 4i?

2. Homework Equations
Integral calculus, vectors

The Attempt at a Solution


I don't understand why one could do this. The integral is of E and dA, not E and A. How can I use A to determine dA?

This is a crackpot way I thought of

[tex] \Phi = \int \vec{E} \cdot \vec{dA} [/tex]

[tex]
\Phi = \vec{E} \cdot \int \vec{dA}
[/tex]

[tex]
\Phi = \vec{E} \cdot \vec{A}
[/tex]

Then Phi = 4i dot (2i + 3j) = 8 flux units

This seems like wild fantasy though as I don't know if I can pull out a constant from a dot product integral
 
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  • #2
There is no dA to speak of. You are given A which is the same everywhere and E which is uniform. Just take the dot product as you have in your third equation. There isn't much to this problem/
 
  • #3
.


Your approach is correct. The integral for flux is given by the dot product of the electric field and the area vector, which in this case is simply the dot product of E and A. This is because the electric field is uniform and perpendicular to the surface, so the magnitude of the electric field is constant over the entire surface. Therefore, we can pull out the constant E and integrate only the area vector to get the flux. Your calculation of 8 flux units is correct.
 

1. What is Flux?

Flux is a mathematical concept related to the flow of a physical quantity through a surface or region. It is often used in physics and engineering to calculate things like electric or magnetic fields.

2. How do you calculate Flux?

To calculate Flux, you need to take an integral of the product of a vector field and the surface or region over which it is flowing. This gives you a numerical value that represents the amount of flow through that surface or region.

3. What is the difference between Flux and Flux Density?

Flux density is the amount of Flux per unit area, whereas Flux is the total amount of flow through a given surface or region. Flux density is a vector quantity, while Flux is a scalar quantity.

4. Can Flux be negative?

Yes, Flux can be negative if the vector field and the surface or region are oriented in opposite directions. This means that the flow is going in the opposite direction of the surface or region's normal vector.

5. What are some applications of Flux?

Flux has many applications in physics and engineering. It is used to calculate things like electric or magnetic fields, fluid flow, and heat transfer. It is also used in differential equations and in the study of fluid dynamics.

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