$A$ solenoid having area $A$ and length $l$ is filled with a material having relative permeability $2$. The magnetic energy stored in the solenoid is

In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

$A$ solenoid is $1.5 \, m$ long and its inner diameter is $4.0 \, cm$. It has three layers of windings of $1000$ turns each and carries a current of $2.0 \, A$. The magnetic flux for a cross-section of the solenoid is nearly:

$A$ long straight wire of a circular cross-section with radius $a$ carries a steady current $I$. The current $I$ is uniformly distributed across this cross-section. The plot of the magnitude of the magnetic field $B$ with distance $r$ from the centre of the wire is given by:

$A$ current $I$ flows along the length of an infinitely long,straight,thin-walled pipe. Then:

$A$ 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.