Question

Fig. shows a torodial solenoid whose cross-section is rectangular. Find the magnetic flux through this cross-section if the current through the winding equals $I=1.7A$, the total number of turns is $N=1000$, the ratio of the outside diameter to the inside one is $\eta =1.6$, and the height is equal to $h=5.0cm$.

Answer 1

$B_{\phi }2\pi r={\mu }_{0}nI$
or, $B_{\phi }=\frac{{\mu }_{0}nI}{2\pi r}$
Then,
$\Phi ={\int }_a^b{B}_{\phi }hdr,a\le r\le b=\frac{{\mu }_0}{4\pi }2NIh\ln \eta$, where $\eta =\frac{b}{a}$
$\Phi ={10}^{-7}\times 2\times 1000\times 1.7\times (5\times {10}^{-2})\times \ln \left(1.6\right)=8\times {10}^{-6}Wb=8\mu Wb$