$A$ $90\, cm$ long solenoid has six layers of windings of $450\, turns$ each. If the diameter of the solenoid is $2.2\, cm$ and the current carried is $6\, A$, then the magnitude of the magnetic field inside the solenoid, near its centre is: (in $\pi\, G$)

Two long conductors are arranged as shown above to form overlapping cylinders,each of radius $r$,whose centers are separated by a distance $d$. Current of density $J$ flows into the plane of the page along the shaded part of one conductor and an equal current flows out of the plane of the page along the shaded portion of the other,as shown. What are the magnitude and direction of the magnetic field at point $A$?

$A$ long solenoid has a radius $a$ and the number of turns per unit length is $n$. If it carries a current $i$,then the magnetic field on its axis is directly proportional to

What are the directions of the magnetic field between and outside a pair of two parallel large sheets carrying currents in the same directions,as illustrated in the figure?

$A$ solenoid has a core of a material with relative permeability $400$. The windings of the solenoid are insulated from the core and carry a current of $1 \text{ A}$. If the number of turns is $1000 \text{ per metre}$,the magnetic field $(B)$ is . . . . . . $\text{T}$. (Given: $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$)

$A$ toroid has $500$ turns per metre length. If it carries a current of $2 \text{ A}$, the magnetic energy density inside the toroid is: (in $\text{ J/m}^3$)