A circular coil carrying a current has radius $\mathrm{R}$. The ratio of magnetic induction at the centre of the coil and at a distance equal to $\sqrt{3}\mathrm{R}$ from the centre of the coil on the axis is

Two thin metal strips, carrying current in the directions shown, cross each other perpendicular without touching but being close to each other, as shown in Fig. The regions which contain some points of zero magnetic induction are

A wire of length $\mathrm{l}$ is bent into a circular coil of one turn of radius ${\mathrm{R}}_1$. Another wire of the same material and same area of cross-section and same length is bent into a circular coil of two turns of radius ${\mathrm{R}}_2$. When the same current flows, through the two coils, the ratio of magnetic induction at the centres of the two coils is

The figure fig.$8.115$ shows the cross-section of a long cylindrical conductor of radius $a$ carrying a uniformly distributed current $𝔦$. The magnetic field due to current at $P$ is 

A wire shown in figure Fig. $8.116$ carries a current of $40 \mathrm{A}$. If $r=3.14 \mathrm{cm}$, the magnetic field at the point $P$ will be

Two long parallel conductors carry currents in opposite directions as shown in Fig. $8.117$. One conductor carries a current of $10 \mathrm{A}$ and the distance between the wires is $d=10 \mathrm{cm}$ Current $I$ is adjusted, so that the magnetic field at $P$ is zero. $P$ is at a distance of $5 \mathrm{cm}$ to the right of the $10 \mathrm{A}$ current. Value of $I$ is