# Calculus

find the flux of F=<0,y,z> across the parabolic sheet given by x=2y^2+2z^2+3, with x <= 5

1. 👍 0
2. 👎 0
3. 👁 164
1. Flux = I = ∫∫F.n dS
for S over the surface, g(x,y,z), where
g(x,y,z) is the part of
x=2y²+2z²+3 where x≤5, which translates to
g(x,y,z)=x-2y²-2z²-3
and the region is the part of the paraboloid where y²+z²≤1 after substitution of x≤5.
This region is circular with radius =1, which facilitates integration later.

Now:
F = <0,y,z>
n=∇g/||g||
so I can be evaluated:
I = ∫∫F.n dS
The surface integral can be evaluated by projecting it to the region R on the y-z plane by multiplying:
dS over S = ||g|| dA over R

So
I = ∫∫F.n dS over S
= ∫∫F.n ||g|| dA over R
where R is the circular region r≤1 in polar coordinates.

The way I have defined g(x,y,z) results in negative flux.

Post if you could use more help.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

A cone is constructed by cutting a sector from a circular sheet of metal with radius 20cm. The cut sheet is then folded up and welded. Find the radius and height of the cone with the maximum volume that can be formed in this way.

asked by Lee Meyer on November 10, 2012
2. ### math

In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 400 m apart, and the lowest point of the suspension cables is 100 m below the top of the towers. Find the

asked by Morgan on October 14, 2014
3. ### Physics

A cube of side a is placed in a uniform field E=6.50 * 10^3 N/C with edges parallel to the field lines. a) whats the net flux through the cube? b) what is the flux through each of its six faces?

asked by Niraj on January 29, 2008

A house has a floor area of 119 m2 and an outside wall that has an area of 32 m2. The earth's magnetic field here has a horizontal component of 2.1 x 10^-5 T that points due north and a vertical component of 5.0 x 10^-5 T that

asked by Mary on November 5, 2007

Find the area lying above the x axis and below the parabolic curve y= 4x -x^2 a.8 b. 8 1/3 c. 10 2/3 d. 16 B or C not sure??

asked by anon on March 5, 2011
1. ### physics

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet 2, and a laser beam is directed onto the sheets from above. The laser beam enters sheet 1 and then strikes the interface between sheet 1

asked by James on March 9, 2016
2. ### Physics

An infinite,insulating sheet has a surface charge density 3.14C/m^2 the height is 12km A.) find the surface area of the Gaussian surface B.) find the total charge C.) find the total electric flux D.) use Guass's law to find the

asked by Macy on February 25, 2015
3. ### Math

A new queen size bed sheet measures 210cm by 240 cm. The lenght and width shrinks by 2 percent after the first wash a. What are the dimensions of the sheet after washing b. What is the percent decrease in the area of the sheet

asked by Haylie on December 16, 2012
4. ### physics

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 98% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes

asked by Anonymous on April 10, 2014
5. ### Physics

Which of the following exhibits parabolic motion? a. a stone thrown into a lake b. a space shuttle orbiting Earth c. a leaf falling from a tree d. a train moving along a flat track what is parabolic motion? which would be a good

asked by y912f on February 5, 2009
6. ### Physics

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 94% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes

asked by Delli on February 15, 2009