The magnetic induction at the centre of a current-carrying circular coil of radius $10 \, cm$ is $5\sqrt{5}$ times the magnetic induction at a point on its axis. The distance of the point from the centre of the coil (in $cm$) is

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$,making an angle $\theta$ with the current element,then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

An infinitely long wire carrying current $I$ is along the $Y$-axis such that its one end is at point $A(0, b)$ while the wire extends up to $+\infty$. The magnitude of the magnetic field strength at point $(a, 0)$ is:

Which of the following graphs shows the variation of magnetic induction $B$ with distance $r$ from a long straight wire carrying current?

Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is

The magnetic field at a distance of $10 \ cm$ from a long straight thin wire carrying a current of $4 \ A$ is (in $\mu T$)