$A$ wire is first bent in the form of a circular coil of $5$ turns and the same wire is then bent in the form of another circular coil of $10$ turns. If the same current is passed in both the coils,then the ratio of the magnetic fields at their centres is

The magnetic field at a point $P$ situated at a perpendicular distance $R$ from a long straight wire carrying a current of $12 \ A$ is $3 \times 10^{-5} \ Wb/m^2$. The value of $R$ in $mm$ is $\left[\mu_0 = 4\pi \times 10^{-7} \ Wb/Am\right]$

$A$ small cube of side $1 \ mm$ is placed at the center of a circular loop of radius $20 \ cm$. If the current in the loop is $2 \ A$,then the magnetic energy stored inside the cube is (Assume $\mu_0 = 4 \pi \times 10^{-7} \ SI$ units).

$A$ non-conducting disc of radius $R$ has a surface charge density which varies with distance from the centre as $\sigma(r) = \sigma_0 \left[1 + \sqrt{\frac{r}{R}}\right]$,where $\sigma_0$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre,then $\frac{B}{\mu_0 \sigma_0 \omega R}$ will be

The magnetic field due to a current-carrying square loop of side $a$ at a point located symmetrically at a distance of $a/2$ from its centre (as shown in the figure) is:

An electron of mass $m$ is revolving around the nucleus in a circular orbit of radius $r$ and has angular momentum $L$. The magnetic field produced by the electron at the centre of the orbit is ($e = \text{electric charge}$, $\mu_{0} = \text{permeability of free space}$)