How to Calculate Magnetic Flux on a Surface Along a Wire?

[YoungILoveYou]

Along a wire (of radius r) a current i is crossed from one.
Calculate the magnetic flux through the surface S, inner to the wire.

http://img138.imageshack.us/my.php?image=cilindrodb4.jpg

I think

$$\phi_b= \int B dS= BS$$

$$B=\mu_0 i/2\pi r$$

How to calculate S if I have not the length of wire?

The solution of the problem is
$$\phi_b=\mu_0 i /4\pi$$

 

[Astronuc]

If this is a wire 'loop' of radius r, then the length is simply 2$\pi$r, and the area circumscribed by a circle is given by A = $\pi$r².

 

[YoungILoveYou]

Area=S

S is a rectangular (see image linked) surface, it is not a circle.

S would be the Area of a rectangular of base R and height=length of wire (infinite)