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:

If the strength of the magnetic field produced $10\,cm$ away from an infinitely long straight conductor is ${10^{ - 5}}\,Wb/m^2$,the value of the current flowing in the conductor will be........$A$.

$A$ circular loop and an infinitely long straight conductor carry equal currents,as shown in the figure. The net magnetic field at the centre of the loop is $B_1$,when the current in the loop is clockwise and $B_2$ when the current in the loop is anti-clockwise. Then $\frac{B_1}{B_2}$ is

$A$ current of $1 \,A$ is flowing along the sides of an equilateral triangle of side $a = 4.5 \times 10^{-2} \,m$. The magnetic field at the centroid of the triangle is $(\mu_0 = 4 \pi \times 10^{-7} \,T \cdot m/A)$.

Two coils $P$ and $Q$ each of radius $R$ carry currents $I$ and $\sqrt{8} I$ respectively in the same direction. These coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ($\mu_0 =$ permeability of free space).

$A$ thin charged rod is bent into the shape of a small circle of radius $R$, the charge per unit length of the rod being $\lambda$. The circle is rotated about its axis with a time period $T$, and it is found that the magnetic field at a distance $d$ away $(d >> R)$ from the center and on the axis varies as $\frac{R^{m}}{d^{n}}$. The values of $m$ and $n$ respectively are: