Simple Theoretical Question about Ampere's Law

[Lomion]

Hi all,

This one's an easy one: What's the easiest way of telling whether a current is "enclosed" in a closed path or not? And how can I tell when a current effectively cancels itself out?

For example, let's say I have a spherical shell with surface current density K [A/m], and I want to find H outside the sphere. Would this be 0 because whatever total current is over the sphere, the current flowing would eventually cancel each other out. Is this a valid assumption, even for K not constant?

Would the reasoning for something like this be similar to the reasoning for H = 0 outside a solenoid (approximately!) and a toroid?

Any clarifications would be appreciated!

 

[zeronem]

Take a look at the Closed Path. If a current is running through the closed path either going in or out of it, then the current is enclosed in the closed path. If the current is outside of the closed path,, the current is not enclosed in the closed path.

Well, if there are two currents $$I_1$$ and $$I_2$$ running in opposite directions to each other through the enclosed path, then the currents will subtract each other, and depending the amount of amps, depends on whether they completely cancel or don't completely cancel each other out. The Two currents will subtract each other no matter how you do the integration

$$\int B ds$$ clockwise or counterclockwise.

Now if there are more then two currents, then the right hand rule must be used. Depending on which way you integrate depends on which way your use your right hand rule around the closed path. Your Currents being positive or negative depends on the right hand rule(whether you integrate clockwise or counterclockwise).

 

[Lomion]

Take a look at the Closed Path. If a current is running through the closed path either going in or out of it, then the current is enclosed in the closed path. If the current is outside of the closed path,, the current is not enclosed in the closed path.

I know this sounds a bit stupid, but that's exactly what I'm confused about in my first example. Basically, I put a loop outside of the spherical shell. And depending on where I put the loop, it will either enclose the sphere, and hence have current going through it, or not enclose the sphere, and have no current going through it (At any given R). In fact, if I move the loop up or down, it will contain different surface areas of the sphere.

My TA said that since the current was circling on the sphere's surface, then the net current is zero. But I'm sort of having trouble seeing this.

Help?

 

[StatusX]

How is the current flowing? Like lines of latitude, or longitude, or something else? Also, you must also include the changing electric field in the loop because of maxwells correction.