$A$ closely wound solenoid of $1200$ turns and area of cross-section $5 \,cm^2$ carries a current. If the magnetic moment of the solenoid is $1.2 \,J \,T^{-1}$, then the current through the solenoid is (in $\,A$)

Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\overrightarrow{F_1}$ be the magnetic force on the inner solenoid due to the outer one and $\overrightarrow{F_2}$ be the magnetic force on the outer solenoid due to the inner one. Then

$A$ long solenoid has $70 \text{ turns } cm^{-1}$ and carries current $I$. An electron moves within the solenoid in a circle of radius $2.5 \text{ cm}$ perpendicular to the solenoid axis. If the speed of the electron is $4.4 \times 10^6 \text{ m s}^{-1}$, then the current $I$ in the solenoid is (Take $\mu_0 = 4 \pi \times 10^{-7} \text{ SI unit}$, mass of electron $= 9 \times 10^{-31} \text{ kg}$, charge of electron $= 1.6 \times 10^{-19} \text{ C}$) (in $\text{ mA}$)

In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

$A$ coil wrapped around a toroid has an inner radius of $20 \,cm$ and an outer radius of $25 \,cm$. If the wire wrapping makes $800$ turns and carries a current of $12 \,A$, the maximum and minimum values of the magnetic field within the toroid are:

$A$ solenoid has a core made of material with relative permeability $400$. The magnetic field produced in the interior of the solenoid is $1.0 \text{ T}$. The magnetic intensity in $SI$ units is $\alpha \times 10^5$. The value of $\alpha$ is . . . . . . . (Free space permeability $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.)