$A$ closely wound circular coil of radius $5\,cm$ produces a magnetic field of $37.68 \times 10^{-4}\,T$ at its center. The current through the coil is $......A$. [Given,number of turns in the coil is $100$ and $\pi=3.14$]

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is

Two concentric coils each of radius equal to $2\pi \, cm$ are placed at right angles to each other. $3 \, A$ and $4 \, A$ are the currents flowing in each coil respectively. The magnetic induction in $Wb/m^2$ at the centre of the coils will be $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$.

An electron $(e)$ moves in a circular orbit of radius '$r$' with uniform speed '$V$'. It produces a magnetic field '$B$' at the center of the circle. The magnetic field $B$ is ($\mu_0 =$ permeability of free space).

Which one of the following options represents the magnetic field $\vec{B}$ at $O$ due to the current $I$ flowing in the given wire segments lying on the $xy$ plane?

The magnetic field normal to the plane of a coil of $N$ turns and radius $r$ which carries a current $i$ is measured on the axis of the coil at a distance $h$ from the centre of the coil. This is smaller than the field at the centre by the fraction,