$A$ solenoid of $1200$ turns is wound uniformly in a single layer on a glass tube $2\,m$ long and $0.2\,m$ in diameter. The magnetic intensity at the center of the solenoid when a current of $2\,A$ flows through it is:

$A$ long solenoid with $10.0 \text{ turns/cm}$ and a radius of $8 \text{ cm}$ carries a current of $7 \text{ mA}$. $A$ current-carrying straight conductor is located along the central axis of the solenoid. If the direction of the resulting magnetic field is $60^{\circ}$ to the axial direction at a point $5 \text{ cm}$ from the axis of the solenoid along the radial direction, then the current in the conductor is. [Take $\sqrt{2}=1.4, \sqrt{3}=1.7$] (in $\text{ A}$)

$A$ 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 $|q_e| = 1.6 \times 10^{-19} \text{ C}$,$\mu_0 = 4\pi \times 10^{-7} \text{ N/A}^2$,$1 \text{ ns} = 10^{-9} \text{ s}$]

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density $J$ along its length. The magnitude of the magnetic field,$|\vec{B}|$ as a function of the radial distance $r$ from the axis is best represented by:

There are $50$ turns per $cm$ length in a very long solenoid. It carries a current of $2.5 \ A$. The magnetic field at its centre on the axis is . . . . . . $T$.

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