Inductance per unit length near the middle of a long solenoid is ($\mu_0=$ permeability of free space,$n=$ number of turns per unit length,$d=$ the diameter of the solenoid).

$A$ toroid has a non-ferromagnetic core of inner radius $r_{1}$ and outer radius $r_{2}$,around which $N$ turns of wire are wound. If the current in the wire is $I$,then the magnetic field inside the toroid is ($\mu_{0} =$ permeability of free space).

$A$ solenoid $60 \;cm$ long and of radius $4.0\; cm$ has $3$ layers of windings of $300$ turns each. $A$ $2.0 \;cm$ long wire of mass $2.5\; g$ lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of $6.0\; A$ in the wire. What value of current (in $A$) in the windings of the solenoid can support the weight of the wire? $(g=9.8\; m \,s ^{-2})$

$A$ long cylindrical conductor with a large cross-section carries an electric current distributed uniformly over its cross-section. The magnetic field due to this current is:

What is a solenoid? And what is a long solenoid? Explain.

$A$ thick current-carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B(r)$ due to the cable with the distance $r$ from the axis of the cable is represented by: