$A$ solenoid of $1000$ turns is wound uniformly on a glass tube $4 \text{ m}$ long and $0.3 \text{ m}$ in diameter. The magnetic intensity at the centre of the solenoid when a current of $4 \text{ A}$ 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 $\text{ A}$)

The magnetic field at the centre of a long solenoid having $400$ turns per unit length and carrying a current $i$ is $6.24 \times 10^{-2} \,T$. The magnetic field at the centre of another long solenoid having $200$ turns per unit length and carrying a current $\frac{i}{2}$ is

The magnetic field intensity $(H)$ at the centre of a long solenoid having '$n$' turns per unit length and carrying a current $I$, when no material is kept in it is ($\mu_0$ = permeability of free space)

$A$ particle of mass $2.2 \times 10^{-30} \,kg$ and charge $1.6 \times 10^{-19} \,C$ is moving at a speed of $10 \,km/s$ in a circular path of radius $2.8 \,cm$ inside a solenoid. The solenoid has $25 \,turns/cm$ and its magnetic field is perpendicular to the plane of the particle's path. The current in the solenoid is (Take $\mu_0 = 4\pi \times 10^{-7} \,H/m$) (in $\,mA$)

The magnetic field intensity $H$ at the centre of a long solenoid having $n$ turns per unit length and carrying a current $I$,when no material is kept in it,is