An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface. Choose the correct representation of magnetic field $(B)$ as a function of radial distance $(r)$ from the axis of the cylinder.

$A$ closely wound solenoid $120 \ cm$ long has $4$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8 \ cm$. If the current carried is $8.0 \ A$,estimate the magnitude of $B$ inside the solenoid near its centre.

$A$ current of $1/4\pi \ A$ is flowing through a toroid. It has $1000$ turns per meter. The value of the magnetic field (in $Wb/m^2$) along its axis is:

$A$ solenoid of length $0.5 \,m$ has a radius of $1 \,cm$ and is made up of $m$ number of turns. It carries a current of $5 \,A$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \,T$, then the value of $m$ is:

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current,the variation of magnetic field in the inside and outside region of the wire is :

$A$ long solenoid has $200$ turns per $cm$ and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2} \ Wb/m^2$. Another long solenoid has $100$ turns per $cm$ and it carries a current $i/3$. The value of the magnetic field at its centre is: