Ampere's circuital law is associated with which law?

The magnetic field intensity inside a current-carrying solenoid is $H = 2.4 \times 10^3 \ A/m$. If the length and the number of turns of the solenoid are $15 \ cm$ and $60$ turns respectively,the current flowing in the solenoid is: (in $A$)

The magnetic field intensity $(H)$ at the centre of a long solenoid carrying a current of $2 \ A$ is found to be $1000 \ A/m$. The number of turns per centimeter of the solenoid is: (Use $\mu_0 = 4 \pi \times 10^{-7} \ T \ m \ A^{-1}$)

$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per $cm$ is doubled and the current is made $\left(\frac{1}{3}\right)^{rd}$ of its original value,then the new value of the magnetic field will be:

The relative permeability in a core of a solenoid is $400$. The windings of a solenoid are insulated from the core and carry a current of $2 \ A$. If the number of turns is $1000$ per meter,then the magnetic intensity inside the core of the solenoid is . . . . . . $\frac{A}{m}$.

$A$ toroid has a number of turns per unit length $n$ and current $i$. What is the magnetic field inside the toroid?