The electric current in a circular coil of $2$ turns produces a magnetic induction $B_{1}$ at its centre. The coil is unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction $B_{2}$ at its centre. The ratio of $\frac{B_{2}}{B_{1}}$ is:

Two long parallel straight metal wires $A$ and $B$ carrying currents $12 \,A$ and $36 \,A$ respectively,in the same direction are separated by $50 \,cm$. The point relative to $A$,where the resultant magnetic induction between the two wires due to the currents is zero,will be (in $\,cm$)

Which of the following statements is false for Helmholtz coils?

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: $\left[\mu_0 = 4\pi \times 10^{-7} \text{ H/m}, q = 1.6 \times 10^{-19} \text{ C}\right]$

$A$ current-carrying circular loop of radius '$R$' and a current-carrying long straight wire are placed in the same plane. The currents through the circular loop and the long straight wire are '$I_C$' and '$I_w$' respectively. The perpendicular distance between the centre of the circular loop and the wire is '$d$'. The magnetic field at the centre of the loop will be zero when the separation '$d$' is equal to:

Apply the Biot-Savart law to find the magnetic field due to a circular current-carrying loop at a point on the axis of the loop.