# Flux in open cylinder

1. May 3, 2009

### -EquinoX-

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

A vector field $$\vec{G}$$ in 3-space is defined outside the cylinder $$x^2 + y^2 = 4$$

$$\vec{G} = \frac{6y\vec{i}-6x\vec{j}}{x^2+y^2}$$

Find $$\int\limits_S \vec{G} \cdot · d\vec{A}$$ where S is the open cylinder $$x^2 + y^2 = 16 , 0 \leq z \leq 7$$ oriented outward.

2. Relevant equations

3. The attempt at a solution

I am planning to use divergence theorem here... can I use it?

2. May 3, 2009

### Marco_84

use also cilndric coordinates ;)

3. May 3, 2009

### -EquinoX-

it's kind of hard to find the divergence here... is it just:

$$\frac{24xy}{(x^2+y^2)^2}$$

at least that's what I got. How do I parametrize the open cylinder?

4. May 4, 2009

### mitchturb

What does it mean defined outside the cylinder?

5. May 5, 2009

### -EquinoX-

I am actually confused my self with that... as far as my understanding goes it just means the direction points outwards...

someone care to correct me and give me more help to solve this problem?

6. May 6, 2009

### Marco_84

Usually it mean that inside the cylinder and on its boundaries the field is null. Think about electrostatics ;)

MM