# Surface Integral

1. Dec 6, 2013

### physics&math

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

The problem asks to find the flux through a cylinder of radius R and height h.

2. Relevant equations

Flux = ∫∫FndS over S

F = (ix + jy)*ln(x2+y2)

3. The attempt at a solution

After finding the unit normal vector (n) to the curved surface of the cylinder, the integral simplified down to:

∫∫((x2+y2)/√(x2+y2))*ln(x2+y2)dS

I'm wondering if it is ok to replace x2+y2 with R2. Then the integral would be:

∫∫Rln(R2)dS

and since R is a constant

Rln(R2)∫∫dS

= 4*pi*hR2ln(R). which is the correct answer

2. Dec 6, 2013

### ShayanJ

Yeah,that's OK because you're computing $\vec{F}\cdot\hat{n}$ only on the surface of the cylinder!