$A$ straight long wire is carrying current $I$. The ratio of magnetic field due to this wire at perpendicular distance $2 \text{ cm}$ and $5 \text{ cm}$ respectively from the wire is

$A$ current of $0.1\, A$ circulates around a coil of $100$ turns and having a radius equal to $5\, cm$. The magnetic field set up at the centre of the coil is $({\mu _0} = 4\pi \times {10^{ - 7}}\,T\cdot m/A)$.

Describe and illustrate the magnetic field lines produced by a current-carrying circular loop.

An electron revolves in a circle of radius $0.4 \text{ Å}$ with a speed of $10^6 \text{ m/s}$ in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron (in Tesla) is: $\left[\mu_0 = 4\pi \times 10^{-7} \text{ H/m}, q = 1.6 \times 10^{-19} \text{ C}\right]$

Two circular loops $L_1$ and $L_2$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_1$ is $R_1$ and that of $L_2$ is $R_2$. The distance between the centres of the loops is $\sqrt{3} R_1$. The magnetic field at the centre of $L_2$ shall be zero if

Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is