$A$ long solenoid is formed by winding $70$ turns $cm^{-1}$. If $2.0\,A$ current flows,then the magnetic field produced inside the solenoid is $.......\times 10^{-4}\,T$ $\left(\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}\right)$

$A$ current-carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of the solenoid. If $g$ is the acceleration due to gravity,then the acceleration $(a)$ of the charged particle will satisfy:

If $B$ is the magnetic field and $\mu_0$ is the permeability of free space,then the dimensions of $(B / \mu_0)$ are:

The magnetic flux near the axis and inside the air core solenoid of length $80 \text{ cm}$ carrying current $I$ is $1.57 \times 10^{-6} \text{ Wb}$. Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length, $\mu_0 = 4\pi \times 10^{-7} \text{ SI unit}$, $\pi = 3.14$). (in $\text{ Am}^2$)

$A$ toroid has a core (non-ferromagnetic) of inner radius $25 \; cm$ and outer radius $26 \; cm,$ around which $3500$ turns of a wire are wound. If the current in the wire is $11 \; A$,what is the magnetic field:
$(a)$ outside the toroid,
$(b)$ inside the core of the toroid,and
$(c)$ in the empty space surrounded by the toroid?

$A$ long thin hollow metallic cylinder of radius $R$ carries a current $i$ ampere. The magnetic induction $B$ at a distance $r$ from the axis varies as shown in: