# Why toroid has no magnetic pole?

Our teacher taught us about Gauss law of magnetism, $\phi_B=\oint_s{\small{}}\vec {B} .\vec {ds}=0$(being valid because magnetic field line form closed loop, right?) which denies the existence of magnetic monopole.

However, it does not decline the existence of magnet with no pole, and I understood how. Then he told us that one such example is an toroid.

Question:

But, I am not able to understand why does a toroid have no pole? Shouldn't it have a pole similar to circular loop, why it does not? (Please explain this one in detail.)

Also, while thinking about the above, what about a long current carrying conductor? Does it have a pole or not?

(Sorry for the rudimentary question, but high school physics is always like take this and we get that and things, never explains why? It bothers me.)

Thank you!

• I think you mixed up the equation. – b_jonas Dec 29 '14 at 11:20
• Umm, I don't understand. Which equation did i mix up? – Mann Dec 29 '14 at 12:56
• First of all your teacher is wrong. Gauss law doesnt say there cannot be magnetic monopole. Gauss law just mean we havent found an magnetic monopole yet. – Paul Dec 29 '14 at 13:43
• Oh thanks, I will remember that. But I used to think that a magnetic monopole would have net magnetic flux passing, which contradicts the gauss law? Like q was a source of $\vec E$ , then maybe similar with $m$? – Mann Dec 29 '14 at 13:45