Question

Currents flowing in a solenoid and a toroid are $2i$ and $6i$ respectively. If the number of turns per unit length is $2n$ and $n$ respectively. Find the ratio of magnetic field inside the core due to solenoid and toroid.

• A. $1:3$
• B. $3:4$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is C $2:3$

Magnetic field inside the solenoid near to its axis is given by

$B_s={\mu }_0{n}_s{i}_s$

From question, $n_s=2n;i_s=2i$

$\therefore B_s=4{\mu }_{0}ni$

And magnetic field produced by toroid inside the core of toroid is given by

$B_t={\mu }_0{n}_t{i}_t$

From question, $n_t=n;i_t=6i$

$\therefore B_t=6{\mu }_{0}ni$

$\therefore \frac{B_s}{B_t}=\frac{4{\mu }_{0}ni}{6{\mu }_{0}ni}=\frac{2}{3}$

Hence, option (c) is the correct answer.