Question

Current flowing in a solenoid and a toroid is $i$ and $4i$ respectively. If the number of turns per unit length is $3n$ and $n$ respectively. Find the ratio of magnetic field inside the core due to solenoid and toroid.

• A. $4:5$
• B. $3:4$
• C. $12:1$
• D. $1:12$

Answer 1

The correct option is B $3:4$

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

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

From question, $n_s=3n;i_s=i$

$\therefore B_s=3{\mu }_{0}ni$

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

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

From question, $n_t=n;i_t=4i$

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

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

Therefore, option $\left(b\right)$ is correct.