$A$ current $i$ ampere flows along an infinitely long straight thin-walled tube. The magnetic induction at any point inside the tube is:

Two wires carrying currents of $5 \ A$ and $2 \ A$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3 \ A$ is situated outside the loop. The value of $\oint \overrightarrow{B} \cdot d\overrightarrow{l}$ around the loop is ($\mu_0 = \text{permeability of free space}$,$d\overrightarrow{l}$ is the length element of the Amperian loop).

$A$ long solenoid is formed by winding $70$ turns $cm^{-1}$. If $2.0\,A$ current flows,then the magnetic field produced inside the solenoid is $.......\times 10^{-4}\,T$ $\left(\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}\right)$

The current required to be passed through a solenoid of $15\,cm$ length and $60$ turns in order to demagnetize a bar magnet of magnetic intensity $2.4 \times 10^3\,A/m$ is $.........A$.

The magnetic field $(B)$ inside a long solenoid having '$n$' turns per unit length and carrying current '$i$' when an iron core is kept in it,is ($\mu_0 =$ permeability of vacuum,$\chi =$ magnetic susceptibility).

$A$ current-carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of the solenoid. If $g$ is the acceleration due to gravity, then the acceleration $(a)$ of the charged particle will satisfy: