When equal current is passed through two coils,equal magnetic field is produced at their centres. If the ratio of the number of turns in the coils is $8: 15$,then the ratio of their radii will be

Two points $A$ and $B$ on the axis of a circular current loop are at distances of $4 \ cm$ and $3 \sqrt{3} \ cm$ from the centre of the loop. If the ratio of the induced magnetic fields at points $A$ and $B$ is $216: 125$, the radius of the loop is (in $cm$)

$A$ straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is

The magnetic field at the center of a circular coil of radius $0.1\, m$ having $1000$ turns and carrying a current of $0.1\, A$ is:

$A$ coil having $2000$ turns is wound tightly in the form of a spiral with inner and outer radii $1 \,cm$ and $3 \,cm$, respectively. When a current $\frac{1}{\pi} \,mA$ passes through the coil, the magnetic field at the centre is calculated to be $K \ln 3 \times 10^{-6} \,T$. The value of $K$ is

Two long straight conductors with currents $I_1$ and $I_2$ are placed along $X$ and $Y$-axes respectively. The equation of the locus of points of zero magnetic induction is: