Understanding Ampère's Law: How to Solve for Zero Current in a Closed Loop

[Gyroscope]

Homework Statement

Would someone, please, show me that, if there is no current inside, that:

$$\oint \vec B \cdot d\vec l=0$$

Please. Thanks.

Homework Equations

The Attempt at a Solution

 

[marcusl]

You can do this yourself! First use Stokes's theorem to relate your integral to a surface integral over curl(B), then substitute Maxwell's eqn. for curl(B). Note what happens if J and dD/dt are zero.

 

[Gyroscope]

I do not know Stokes Theorem. :) I am preparing to IPHO.