$A$ circular loop of radius $0.0157\,m$ carries a current of $2.0\,A$. The magnetic field at the centre of the loop is $(\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A)$.

$A$ thin ring of radius $R$ meter 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 in $Wb/m^2$ at the center of the ring is $(\mu_0 = \text{Permeability of free space})$

An element $\overrightarrow{\Delta \ell} = \Delta x \hat{i}$ is placed at the origin and carries a current of $10 \ A$. Find the magnitude of the magnetic field on the $Y$-axis at a distance of $0.5 \ m$,given $\Delta x = 1 \ cm$. (Use $\frac{\mu_0}{4 \pi} = 10^{-7} \ T \cdot m/A$)

$A$ 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 $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$

As shown in the figure,a long straight conductor with a semicircular arc of radius $R = \frac{\pi}{10} \, m$ is carrying a current $I = 3 \, A$. The magnitude of the magnetic field at the center $O$ of the arc is $........... \mu T$. (The permeability of the vacuum $\mu_0 = 4 \pi \times 10^{-7} \, T \cdot m/A$)

Two long parallel wires carry currents $I_1$ and $I_2$ $(I_1 > I_2)$. When currents are flowing in the same direction,the magnetic field at a point midway between the wires is $6 \times 10^{-6} \ T$. If the direction of $I_2$ is reversed,the field at the midpoint becomes $3 \times 10^{-5} \ T$. The ratio $I_1 : I_2$ is