Calculating Flux Across a Portion of a Surface in the First Octant

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In summary, to find the flux of the given vector field across the given surface, we need to integrate the dot product of the vector field and the unit normal vector. The surface is defined as the portion of y=e^x in the first octant projected parallel to the x-axis onto a rectangle with boundaries 1 <= y <= 2 and 0<= z <= 3. The unit normal vector n is pointing away from the yz-plane.
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robierob
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Find the flux of the field F=(-2x,3y,Z) across the surface S where S is the portion of y=(e^x) in the first octant that projects parallel to x-axis onto the rectangle with 1 <= y <= 2 and 0<= z <= 3. Define the unit normal vector n to point away from the yz-plane.

Im not exactly sure about what formula to use for this one...

Rob
 
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Sounds like you want to integrate the dot product of that vector field with the unit normal across the surface, right? What would the general equation be? And have you sketched what the surface and its boundaries look like?
 

FAQ: Calculating Flux Across a Portion of a Surface in the First Octant

What is flux and why is it important in science?

Flux refers to the flow of a physical quantity through a given surface. It is important in science because it allows us to measure and understand the amount of a quantity that is passing through a particular area, which is crucial in many fields such as physics, engineering, and chemistry.

How is flux calculated?

Flux is calculated by multiplying the magnitude of the field by the area of the surface that it is passing through and then taking the dot product of these two values. This gives us the total amount of the quantity passing through the surface in a given time.

What are some common units for flux?

The most common units for flux are Newtons per meter squared (N/m2) in SI units and pounds per square inch (psi) in imperial units. Other units may be used depending on the specific quantity being measured, such as watts per square meter (W/m2) for radiant flux.

How does the direction of the field affect the flux?

The direction of the field is an important factor in calculating flux because it determines the angle at which the field is passing through the surface. The flux will be highest when the field is perpendicular to the surface and will decrease as the field becomes more parallel to the surface.

Can flux be negative?

Yes, flux can be negative. This occurs when the field and the surface have opposite directions, resulting in a negative dot product. A negative flux value indicates that the quantity is leaving the surface rather than entering it.

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