Due to $10 \ A$ of current flowing in a circular coil of $10 \ cm$ radius,the magnetic field produced at its centre is $3.14 \times 10^{-3} \ Wb/m^2$. The number of turns in the coil will be:

The magnetic field at the origin due to a current element $i \, d\vec{l}$ placed at position $\vec{r}$ is given by the Biot-Savart Law. Which of the following expressions correctly represent this magnetic field?
$(i) \, \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{d\vec{l} \times \vec{r}}{r^3} \right)$
$(ii) \, - \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{d\vec{l} \times \vec{r}}{r^3} \right)$
$(iii) \, \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{\vec{r} \times d\vec{l}}{r^3} \right)$
$(iv) \, - \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{\vec{r} \times d\vec{l}}{r^3} \right)$

Two long parallel wires carrying currents $I_1 = 4 \ A$ and $I_2 = 3 \ A$ in opposite directions are placed at a distance of $d = 5 \ cm$ from each other. $A$ point $P$ is at equidistance from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of the magnetic field at point $P$ is ( $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$ ).

At what distance from wire '$B$' does the magnetic field become zero?

What is the ratio of the magnetic field at point $O$ in the given figures?

Magnetic field due to a ring having $n$ turns at a distance $x$ on its axis is proportional to (if $r$ = radius of ring)