$A$ 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).

$A$ long copper tube of inner radius $R$ carries a current $i$. The magnetic field $B$ inside the tube is

$A$ magnetic field of $100 \;G$ $(1 \;G = 10^{-4} \;T)$ is required which is uniform in a region of linear dimension about $10 \;cm$ and area of cross-section about $10^{-3} \;m^2$. The maximum current-carrying capacity of a given coil of wire is $15 \;A$ and the number of turns per unit length that can be wound round a core is at most $1000 \;turns \;m^{-1}$. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

$A$ long,straight wire of radius $a$ carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and $2a$ respectively from the axis of the wire is

The magnetic field intensity $H$ at the centre of a long solenoid having $n$ turns per unit length and carrying a current $I$,when no material is kept in it,is

$A$ 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: