$A$ circular coil of wire consisting of $100$ turns each of radius $9 \ cm$ carries a current of $0.4 \ A$. The magnitude of the magnetic field at the centre of the coil is $[\mu_0 = 12.56 \times 10^{-7} \text{ SI Units}]$.

$A$ single current-carrying loop of wire with current $I$ flowing in an anticlockwise direction when seen from the $+ve\;z$ direction,lying in the $xy$ plane,is shown in the figure. The plot of the $\hat{j}$ component of the magnetic field $(B_y)$ at a distance $a$ (less than the radius of the coil) on the $yz$ plane versus the $z$ coordinate looks like:

Two concentric coils $X$ and $Y$ of radii $16 \, cm$ and $10 \, cm$ lie in the same vertical plane containing $N-S$ direction. Coil $X$ has $20$ turns and carries $16 \, A$. Coil $Y$ has $25$ turns and carries $18 \, A$. Coil $X$ has current in anticlockwise direction and coil $Y$ has current in clockwise direction for an observer looking at the coils facing the west. The magnitude of the net magnetic field at their common centre is:

$B_{X}$ and $B_{Y}$ are the magnetic fields at the centre of two coils $X$ and $Y$ respectively,each carrying equal current. If coil $X$ has $200$ turns and $20 \ cm$ radius and coil $Y$ has $400$ turns and $20 \ cm$ radius,the ratio of $B_{X}$ and $B_{Y}$ is:

Two long parallel wires separated by $0.1 \ m$ carry currents of $1 \ A$ and $2 \ A$, respectively, in opposite directions. $A$ third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of

The figure below shows three circuits consisting of concentric circular arcs and straight radial lines. The center of the circle is shown by the dot. The same current flows through each of the circuits. If $B_1, B_2, B_3$ are the magnitudes of the magnetic field at the center, which of the following is true?