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 $\mu_0$)

What is a solenoid? And what is a long solenoid? Explain.

Write the equation of magnetic field on the axis of a current-carrying finite solenoid.

$A$ long solenoid has $200$ turns per $cm$ and carries a current of $2.5 \ A$. The magnetic field at its centre is $(\mu_0 = 4\pi \times 10^{-7} \ \text{Wb/A} \cdot \text{m})$.

$A$ long solenoid has $200$ turns per cm and carries a current of $2.5 \, A$. The magnetic field at its centre is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A$):

$A$ steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement$(s)$ is (are) :
$(A)$ In the region $0 < r < R$,the magnetic field is non-zero.
$(B)$ In the region $R < r < 2R$,the magnetic field is along the common axis.
$(C)$ In the region $R < r < 2R$,the magnetic field is tangential to the circle of radius $r$,centered on the axis.
$(D)$ In the region $r > 2R$,the magnetic field is non-zero.