Magnetic Flux through a solenoid

[Interesting]

Homework Statement

The magnetic field inside a cylindrical solenoid of area 4 cm^2 is 0.15 T along the axis of the solenoid. What is the magnetic flux through a disk of radius 3 cm placed perpendicular to the solenoid axis?

Homework Equations

\phi = \zeta B * dA

The Attempt at a Solution

Well the area is 4 cm^2 and B is 0.15, so 6E-5 Wb is the answer, but I'm a little confused here. I thought flux for a closed surface was always 0 (gauss' law for magnetism)? What's going on here?

 

[alphysicist]

Homework Statement

The magnetic field inside a cylindrical solenoid of area 4 cm^2 is 0.15 T along the axis of the solenoid. What is the magnetic flux through a disk of radius 3 cm placed perpendicular to the solenoid axis?

Homework Equations

\phi = \zeta B * dA

The Attempt at a Solution

Well the area is 4 cm^2 and B is 0.15, so 6E-5 Wb is the answer, but I'm a little confused here. I thought flux for a closed surface was always 0 (gauss' law for magnetism)? What's going on here?

A closed surface means that it encloses a volume. A sphere, cube, etc. would be a closed surface, but a disk would not. If you constructed a cylinder with the disk in the problem at one end, and calculated the flux through the cylinder then the flux would be zero.