What is the magnetic field inside a toroid having $0.1 \ m$ radius and $500$ turns when a current of $0.5 \ A$ is passed through it?

$A$ $25\,cm$ long solenoid has radius $2\,cm$ and $500$ total number of turns. It carries a current of $15\,A.$ If it is equivalent to a magnet of the same size and magnetization $\vec M$ (magnetic moment per unit volume),then $\left| {\vec M} \right|$ is

The magnetic field inside a current-carrying toroidal solenoid is $0.2 \ mT$. What is the magnetic field inside the toroid if the current is tripled (in $mT$)?

Two coaxial solenoids $1$ and $2$ of the same length are placed such that one is inside the other. The number of turns per unit length are ${n_1}$ and ${n_2}$. The currents ${i_1}$ and ${i_2}$ are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when:

State Ampere's circuital law and explain its mathematical expression.

$A$ toroidal solenoid with air core has an average radius $R$,number of turns $N$,and area of cross-section $A$. The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid).