What is the Magnetic Field of a Toroidal Solenoid?

[frostchaos123]

Homework Statement

A toroidal solenoid has inner radius r1=15.0 cm and outer radius r2=18.0 cm. the solenoid has 250 turns and carries a current of 8.50 A. what is the magnitude of the magnetic field at the following distances from the center of the torus (a) 12.0 cm; (b) 16.0 cm; (c) 20.0 cm?

Homework Equations

Using Ampere's Law, B(2*pi*r) = \muNI

The Attempt at a Solution

The answer given is that if r < r1, the B is 0 as the I enclosed is 0.

However what i do not understand is that why is when r > r2, the I enclosed is also 0?
If r > r2, shouldn't the circle formed encompass the entire solenoid and thus all of the current?

Thanks.

 

[supratim1]

No. its because again the total current THROUGH the area is 0. current going inwards through one turn is canceled by the current coming outwards in the next turn. try to imagine, did you get it?

 

[frostchaos123]

No. its because again the total current THROUGH the area is 0. current going inwards through one turn is canceled by the current coming outwards in the next turn. try to imagine, did you get it?

Not quite sure, but just to double confirm, is my representation of the amperian loop in red correct for r > r2? So do you mean that the current going into the page at the right hand side of the solenoid is canceled by the current coming out of the page on the left hand side?

[URL]http://img130.imageshack.us/i/solenoid.gif/[/URL]

 

[supratim1]

no. every turn's upper part cancels the current of the lower part. got it?

 

[frostchaos123]

ok, i got it, apparently i got the magnetic field and the current flow mixed up.

So to summarise if the loop is bigger than r2, there will be a portion of the current flowing into the surface, and another equal portion coming out of the surface enclosed by the loop

And if the loop is between r1 and r2, then according to the diagram there will be just 1 portion of the current going into the surface and none out.