Question

When calculating the magnetic field of a toroid with turns N at radius r, which sits between an outer radius b and inner radius a, why are a and b added instead of subtracted?

Answer 1

How are you doing it? Using Ampere's Law\[\int\limits_{loop}^{}B*ds=B \int\limits_{loop}^{}ds=B(2 \pi r)=\mu _{0}NI\]where* represents a vector dot product\[B=\frac {\mu _{0}NI} {2 \pi r}\]

Answer 2

I get this, but the answers involve (a+b) instead of r; any idea why this is?

Answer 3

are they asking for field or flux?

Answer 4

magnetic field

Answer 5

Perhaps the answer you cite is being expressed in terms of a and b, not r, with (a+b)/2 standing in for middle value of r. So you might see, instead of 1/r, 2/(a+b).