Calculate Vector Field Flux Through Sphere S of Radius 1

In summary, the conversation discusses calculating the flux through a sphere with a given vector field, using the formula \Phi = \int_{S} \overrightarrow{C}\cdot d\overrightarrow{A}. The person is unsure how to proceed without knowledge of multivariable calculus, but it is mentioned that this particular calculation does not require calculus. The question of what r.dn is on a sphere is also brought up.
  • #1
michael892
3
0
Given is vector field
[tex]\overrightarrow{C}(\overrightarrow{r})=r[/tex]
calculate flux
[tex]\Phi =\int_{S} \overrightarrow{C}\cdot d\overrightarrow{A}[/tex]
through sphere S with beginning in [0,0,0] and r=1
 
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  • #2
welcome to pf!

hi michael892! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
i know i had to calculate surface integral but i didnt have multivariable calculus yet
 
  • #4
hih michael892! :smile:

(just got up :zzz:)
michael892 said:
i know i had to calculate surface integral but i didnt have multivariable calculus yet

you won't need calculus, it's not complicated enough for that

what is r.dn on a sphere of radius r ? :wink:

(where n is the outward normal unit vector)
 

FAQ: Calculate Vector Field Flux Through Sphere S of Radius 1

What is a vector field?

A vector field is a mathematical concept that assigns a vector to every point in a given space. In other words, it describes the direction and magnitude of a physical quantity at every point in space.

What is flux?

Flux is a measure of the flow of a vector field through a given surface. It is calculated by taking the dot product of the vector field and the surface's normal vector and integrating over the surface.

How do you calculate the vector field flux through a sphere?

To calculate the vector field flux through a sphere, you first need to find the vector field's divergence (the rate at which the field spreads out or converges at a given point). Then, you can use the divergence theorem to convert the surface integral into a triple integral, which can be solved using spherical coordinates. Finally, you can plug in the values for the radius and surface area of the sphere to get the final flux value.

What is the significance of a radius 1 sphere in this calculation?

A radius 1 sphere is used in this calculation because it is a standard unit for measuring distance in three-dimensional space. This allows for a simplified and standardized way of calculating the vector field flux through a sphere.

What are some real-world applications of calculating vector field flux through a sphere?

Calculating vector field flux through a sphere has numerous real-world applications, such as calculating fluid flow through a spherical container, calculating the electric or magnetic field strength around a spherical object, and predicting the spread of pollutants through the atmosphere using weather data.

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