The magnetic energy stored in a long solenoid of area of cross-section $A$ in a small region of length $L$ is

$A$ current $i$ ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable. The magnetic induction at any point outside the conductor at a distance $r$ metre from the axis is

$A$ thick uniformly charged hollow cylinder of inner radius $a$ and outer radius $b$ rotates with constant angular speed $\omega$ about its axis $APB$,with charge density $\rho$. Given that $L \gg a$ and $L \gg b$,and $P$ is the midpoint of $AB$. Choose the incorrect option.

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

$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the current is doubled and the number of turns per cm is halved,the new value of the magnetic field is

$A$ solenoid of $1000$ turns per metre has a core of material with relative permeability $400$. The windings of the solenoid are insulated from the core and a current of $2 \ A$ is passed through the solenoid. Then the value of the magnetic intensity inside the solenoid is