Surface Integral Homework: Flux Through a Cylinder

[physics&math]

Homework Statement

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

Homework Equations

Flux = ∫∫FndS over S

F = (ix + jy)*ln(x²+y²)

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

 

[ShayanJ]

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