Vector Calculus II: Flux Integrals

In summary, the problem involves calculating the flux of a vector field through a disk of radius 5 in the plane y=2, oriented in the direction of increasing y. To solve this, the area vector of the surface needs to be calculated and then dotted with F. The area vector is found by multiplying the unit normal by the area element in the plane. The original poster was able to solve the problem with the help provided.
  • #1
Tylerdhamlin
12
0

Homework Statement




F = 2i + 3j through a disk of radius 5 in the plane y = 2 oriented in the direction of increasing y.
Calculate the flux of the vector field through the surface.


Homework Equations





The Attempt at a Solution



I know that I need to calculate the area vector of the surface and then dot that with F, However, I'm in a bit of a brain slump and can't figure out how to calculate the Area Vector.
 
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  • #2
Well, in the simple case of a planar (flat) area, the area vector is the unit normal multiplied by the usual area element in that plane.
 
  • #3
Yes. Shortly after the post, I was able to solve this problem. Anyways, thank you for your help.
 

FAQ: Vector Calculus II: Flux Integrals

1. What is a flux integral in vector calculus?

A flux integral in vector calculus is a mathematical concept that calculates the flow of a vector field through a surface. It measures the rate at which the vector field is passing through the surface, taking into account both the magnitude and direction of the field.

2. How is a flux integral calculated?

A flux integral is calculated by taking the dot product of the vector field and the unit normal vector of the surface, and then integrating over the surface using a double or triple integral depending on the dimensionality of the problem. The resulting value is the total flux through the surface.

3. What are some real-world applications of flux integrals?

Flux integrals have various applications in physics and engineering, such as calculating the flow of fluid through a surface, determining the electric or magnetic flux through a surface, and calculating the rate of heat transfer through a surface.

4. How is a flux integral related to the Divergence Theorem?

The Divergence Theorem states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the region enclosed by the surface. This means that a flux integral can be calculated by evaluating the divergence of the vector field over the region enclosed by the surface.

5. Are there any important limitations to consider when using flux integrals?

Yes, there are some limitations to consider when using flux integrals. One limitation is that the surface must be smooth and well-defined, otherwise the integral may not be accurate. Additionally, the vector field must be continuous and differentiable at all points on the surface for the flux integral to be valid.

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