The magnetic field at the center of a circular coil of radius $0.1\, m$ having $1000$ turns and carrying a current of $0.1\, A$ is:

$A$ square frame of side $l$ carries a current $i$. The magnetic field at its centre is $B$. The same current is passed through a circular coil having the same perimeter as the square. The field at the centre of the circular coil is $B^{\prime}$. The ratio of $\frac{B}{B^{\prime}}$ is

$A$ circular loop of a wire and a long straight wire carry currents $I_c$ and $I_e$,respectively,as shown in the figure. Assuming that these are placed in the same plane,the magnetic field will be zero at the centre of the loop when the separation $H$ is:

$A$ thin ring of radius $R$ metre has charge $q$ coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $f$ revolution/s. The value of magnetic induction at the centre of the ring in $\text{Wb/m}^2$ is ($\mu_0$ = permeability of free space)

The strength of the magnetic field at a point $r$ near a long straight current-carrying wire is $B$. The field at a distance $\frac{r}{2}$ will be

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?