Rank the value of $\oint \vec{B} \cdot d\vec{l}$ for the closed paths shown in the figure from the smallest to largest.

$A$ tightly wound long solenoid carries a current of $1.5 \text{ A}$. An electron is executing uniform circular motion inside the solenoid with a time period of $75 \text{ ns}$. The number of turns per metre in the solenoid is . . . . . . .
[Take mass of electron $m_e = 9 \times 10^{-31} \text{ kg}$,charge of electron $|q_e| = 1.6 \times 10^{-19} \text{ C}$,$\mu_0 = 4\pi \times 10^{-7} \text{ N/A}^2$,$1 \text{ ns} = 10^{-9} \text{ s}$]

What is a solenoid? Provide information about the magnetic field through a qualitative discussion.

$A$ hollow cylinder of infinite length carries a uniform current per unit length $\lambda$ along its circumference,as shown. The magnetic field inside the cylinder is:

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

$A$ very long straight wire of radius $r$ carries current $I$. The intensity of the magnetic field $B$ at a point,lying at a perpendicular distance $a$ from the axis is proportional to: (where $a < r$)