Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and

Question

Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current $i$, the radio of the magnetic fields along the two loops is\

Professor PC Thomas Classes · Answer

(a) : For a toroid magnetic field, $B=\mu_{0} n i$ Where, $n=$ number of turns per unit length $=\frac{N}{2 \pi r}$\ Now, $\frac{B_{1}}{B_{2}}=\frac{\mu_{0} n_{1} i}{\mu_{0} n_{2} i}=\frac{n_{1}}{n_{2}}=\frac{N_{1}}{2 \pi r_{1}} 	imes \frac{2 \pi r_{2}}{N_{2}}$\ $\Rightarrow \quad \frac{B_{1}}{B_{2}}=\frac{200}{2 \pi 	imes 40 	imes 10^{-2}} 	imes \frac{2 \pi 	imes 20 	imes 10^{-2}}{100}$\ $\Rightarrow \frac{B_{1}}{B_{2}}=\frac{1}{1} \Rightarrow B_{1}: B_{2}=1: 1$\