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 $cm$)

The magnetic field near a current-carrying conductor is given by

The magnetic field at the centre of a current-carrying circular coil of radius $R$ is $B_c$ and the magnetic field at a point on its axis at a distance $R$ from its centre is $B_a$. The value of $\frac{B_c}{B_a}$ is

Two concentric circular coils $X$ and $Y$ of radii $16\; cm$ and $10\; cm$ respectively,lie in the same vertical plane containing the north to south direction. Coil $X$ has $20$ turns and carries a current of $16\; A$. Coil $Y$ has $25$ turns and carries a current of $18\; A$. The sense of the current in $X$ is anticlockwise,and clockwise in $Y$,for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

$A$ horizontal overhead powerline is at a height of $4\ m$ from the ground and carries a current of $100\ A$ from east to west. The magnetic field directly below it on the ground is: (Given: $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A$)

The source of magnetic field is . . . . . . and source of electric field is . . . . . . .