A cylindrical cavity of diameter a exists inside a cylinder of diameter $2$a 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 :

Magnetic fields at two points on the axis of a circular coil at a distance of $0.05\, m$ and $0.2\, m$ from the centre are in the ratio $8: 1.$ The radius of coil is .......... $m$

A long straight wire, carrying current $I$ is bent at its mid-point to form an angle of $45^{\circ}$. Induction of magnetic field (in tesla) at point $P$, distant $R$ from point of bending is equal to

A uniform circular wire loop is connected to the terminals of a battery. The magnetic field induction at the centre due to $A B C$ portion of the wire will be (length of $A B C=l_1$, length of $A D C=l_2$ )

A charge $q$ coulomb moves in a circle at $n$ revolutions per second and the radius of the circle is $r$ metre; then magnetic field at the centre of the circle is

Due to $10\, ampere$ of current flowing in a circular coil of $10\, cm$ radius, the magnetic field produced at its centre is $3.14 \times {10^{ - 3}}\,Weber/{m^2}$. The number of turns in the coil will be