The magnetic field due to a current-carrying circular coil on its axis at a distance of $\sqrt{2} \,d$ from the centre of the coil is $B$. If $d$ is the diameter of the coil, then the magnetic field at the centre of the coil is: (in $B$)

In the current-carrying conductor $(AOCDEFG)$ as shown,the magnetic induction at the point $O$ is ($R_1$ and $R_2$ are radii of arcs $CD$ and $EF$ respectively,$I$ = current in the loop,$\mu_0$ = permeability of free space).

Two protons $A$ and $B$ move parallel to the $x$-axis in opposite directions with equal speeds $v$. At the instant shown,the ratio of magnetic force and electric force acting on the proton $A$ is ($c=$ speed of light in vacuum).

Consider the circular loop carrying current $i$ as shown in the figure. The magnetic field at the central point $O$ is

Two concentric coils of $20$ turns each are placed in the same plane. Their radii are $30 \text{ cm}$ and $60 \text{ cm}$,and they carry $0.4 \text{ A}$ and $0.6 \text{ A}$ currents,respectively,in opposite directions. The magnetic induction at the centre in tesla is ....... .

$A$ linear wire carries a current $I$. $A$ single-turn loop is formed from it,and the magnetic field at the center is $B$. If a three-turn loop is formed from the same wire,what will be the magnetic field at the center?