$A$ current $i$ is uniformly distributed over the cross section of a long hollow cylindrical wire of inner radius $R_1$ and outer radius $R_2$. The magnetic field $B$ varies with distance $r$ from the axis of the cylinder as:

Two wires with currents $3 \text{ A}$ and $1.5 \text{ A}$ are enclosed in a circular loop $P$. $A$ third parallel wire with current $1 \text{ A}$ is situated outside the loop as shown. All the wires are perpendicular to the plane of the circular loop. The value of $\oint \vec{B} \cdot d\vec{l}$ around the loop is ($\mu_0$ = permeability of free space) (in $\mu_0$)

There is a long cylindrical pipe wire of internal radius $r$ and external radius $R$ carrying current $i$ along its length. The variation of magnetic field with distance from the axis of the wire can be represented by the :-

Assertion: The magnetic field produced by a current-carrying solenoid is independent of its length and cross-sectional area.
Reason: The magnetic field inside the solenoid is uniform.

$A$ 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

$A$ toroid is a long coil of wire wound over a circular core. If $r$ and $R$ are the radii of the coil and toroid respectively,the coefficient of self-induction of the toroid is (The magnetic field in it is uniform and $R >> r$). ($N =$ number of turns of the coil and $\mu_{0} =$ permeability of free space)