$A$ solenoid of length $0.5\; m$ has a radius of $1\; cm$ and is made up of $500$ turns. It carries a current of $5\; A$. What is the magnitude of the magnetic field inside the solenoid?

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field,$|\vec B |$ as a function of the radial distance $r$ from the axis is best represented by:

$A$ current $i$ flows in an infinitely long, straight and thin-walled pipe. Then,

$A$ solenoid of $1000$ turns per metre has a core of material with relative permeability $400$. The windings of the solenoid are insulated from the core and a current of $2 \ A$ is passed through the solenoid. Then the value of the magnetic intensity inside the solenoid is

$A$ current $i$ is uniformly distributed over the cross section of a long hollow cylindrical wire of inner radius $R_1$ and outer radius $R_2$. The magnetic field $B$ varies with distance $r$ from the axis of the cylinder as:

$A$ cylindrical cavity of diameter $a$ exists inside a cylinder of diameter $2a$ as shown in the figure. Both the cylinder and the cavity are infinitely long. $A$ uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12} \mu_0 aJ$,then the value of $N$ is: