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 the same current $i$,the ratio of the magnetic fields along the two loops is

$A$ solenoid of length $0.25 \ m$ has a radius of $1 \ cm$ and is made up of $500$ turns. It carries a current of $2.5 \ A$. What is the magnitude of the magnetic field inside the solenoid? (Take $\mu_0 = 4 \pi \times 10^{-7} \ SI$ units).

Explain Ampere's circuital law.

$A$ tightly wound long solenoid carries a current of $1.5 \text{ A}$. An electron is executing uniform circular motion inside the solenoid with a time period of $75 \text{ ns}$. The number of turns per metre in the solenoid is . . . . . . .
[Take mass of electron $m_e = 9 \times 10^{-31} \text{ kg}$,charge of electron $|q_e| = 1.6 \times 10^{-19} \text{ C}$,$\mu_0 = 4\pi \times 10^{-7} \text{ N/A}^2$,$1 \text{ ns} = 10^{-9} \text{ s}$]

If a long hollow copper pipe carries a current,then the magnetic field is produced:

$A$ solenoid has a core of a material with relative permeability $\frac{800}{\pi}$. The windings of the solenoid are insulated from the core and carry a current of $2 \text{ A}$. If the number of turns is $1000 \text{ turns/m}$, find the magnetic field $B$. (in $\text{ mT}$)