Find the flux due to a vector crossing an open surface

Engineering
Thread starter falyusuf
Start date Mar 4, 2022
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Flux Surface Vector

In summary, flux is a measure of the flow of a vector field through a surface. To calculate the flux, the dot product between the vector field and the unit normal vector of the surface is integrated over the entire surface. This concept has many real-world applications in fields such as physics and engineering. The direction of the vector affects the positivity or negativity of the flux, but not its magnitude. However, flux may have limitations in accurately representing the flow of a vector through a three-dimensional space or if the vector field is not continuous.

Mar 4, 2022

falyusuf

Homework Statement: Attached below.

Relevant Equations: Attached below.

Question:

Equations:

My attempt:

Could someone confirm my answer please?

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May 10, 2022

rude man

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If ## \bf A = rz~ \hat {\bf \theta} ##
then ## \nabla \times \bf A = (z/r)~ \hat {\bf k} - \hat {\bf r} ##
and not what is given.
Different fields ??

1. What is flux?

Flux is a measure of the flow of a physical quantity through a surface. It is typically represented by the symbol Φ and has units of quantity per unit area.

2. What is an open surface?

An open surface is a surface that is not closed or bounded. In other words, it has a boundary that is not a complete loop or curve.

3. How is flux due to a vector crossing an open surface calculated?

The flux due to a vector crossing an open surface is calculated using the dot product of the vector and the normal vector to the surface, multiplied by the area of the surface.

4. What is the significance of finding the flux due to a vector crossing an open surface?

Finding the flux due to a vector crossing an open surface allows us to understand the flow of a physical quantity through a surface. It is particularly useful in fields such as fluid dynamics and electromagnetism.

5. Can the flux due to a vector crossing an open surface be negative?

Yes, the flux can be negative if the vector and the normal vector have opposite directions. This indicates that the flow is in the opposite direction of the normal vector, or out of the surface rather than into it.