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Finding Flux Through a Cylinder with the Divergance Theorom

  • Thread starter FAS1998
  • Start date
1. The problem statement, all variables and given/known data

I’ve attached an image of the problem below.

I need to use the diveragance theorem to find the flux through a cylinder.

Vector field: F(x,y,z) = 4xi

Height: 5

Radius: 3

2. Relevant equations

By the DT, flux is equal to the triple integral of the divergence of the vector field.

3. The attempt at a solution

The divergence of the vector field is 4.

So the flux should be equal to the triple integral of 4 over the region of the cylinder.

Using cylindrical coordinates, I used the bounds 0 to 5 for z, 0 to 3 for r, and 0 to 2pi for theta.

Solving the triple integral then gave me 4(5)(3)(2pi), which was incorrect.

Can somebody help me figure out what I’m doing wrong?
 

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1. The problem statement, all variables and given/known data

I’ve attached an image of the problem below.

I need to use the diveragance theorem to find the flux through a cylinder.

Vector field: F(x,y,z) = 4xi

Height: 5

Radius: 3

2. Relevant equations

By the DT, flux is equal to the triple integral of the divergence of the vector field.

3. The attempt at a solution

The divergence of the vector field is 4.

So the flux should be equal to the triple integral of 4 over the region of the cylinder.

Using cylindrical coordinates, I used the bounds 0 to 5 for z, 0 to 3 for r, and 0 to 2pi for theta.

Solving the triple integral then gave me 4(5)(3)(2pi), which was incorrect.

Can somebody help me figure out what I’m doing wrong?
##3 \times 5 \times 2 \pi## is the surface area of the sides of your cylinder, but you need the volume, not the area.
 

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