$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)^{th}$,then the new value of the magnetic field will be:

Rank the value of $\oint \vec{B} \cdot d\vec{l}$ for the closed paths shown in the figure from the smallest to largest.

$A$ solenoid of $1000$ turns is wound uniformly on a glass tube $4 \text{ m}$ long and $0.3 \text{ m}$ in diameter. The magnetic intensity at the centre of the solenoid when a current of $4 \text{ A}$ flows through it is

$A$ long solenoid of radius $1\,mm$ has $100$ turns per $mm$. If $1\,A$ current flows in the solenoid,the magnetic field strength at the centre of the solenoid is:

In a co-axial straight cable,the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:

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: