The magnetic energy stored in a long solenoid of area of cross-section $A$ in a small region of length $L$ is

Two toroids $1$ and $2$ have total number of turns $200$ and $100$ respectively with average radii $40 \; cm$ and $20 \; cm$ respectively. If they carry the same current $i$,the ratio of the magnetic fields along the two loops is

$A$ 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:

$A$ long solenoid is formed by winding $20$ $turns/cm$. The current necessary to produce a magnetic field of $20$ $mT$ inside the solenoid will be approximately ..... $A$ $(\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m/A})$.

The magnetic induction produced inside an ideal solenoid depends on which of the following quantities?
$(a)$ Number of turns per unit length $(n)$.
$(b)$ Radius of the wire.
$(c)$ Current flowing through it $(I)$.
$(d)$ Permeability of the medium $(\mu)$.

$A$ toroid has a core (non-ferromagnetic) of inner radius $24 \ cm$ and outer radius $26 \ cm$ around which $2000$ turns of a wire are wound. If the current in the wire is $12 \ A$, the magnetic field inside the core of the toroid is: