The fractional change in the magnetic field intensity at a distance $r$ from the centre on the axis of a current-carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $r << a$)

Write the equation for the magnetic field of a current-carrying circular loop at: $(i)$ a point on the axis,and $(ii)$ a point on the plane of the loop at a distance $x$ from the center of the loop.

What is the ratio of the magnetic field at point $O$ in the given figures?

$A$ 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 $(\mu_0 = \text{permeability of free space})$:

$A$ current of $i$ ampere is flowing in an equilateral triangle of side $a$. The magnetic induction at the centroid will be

$A$ dielectric circular disc of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$,the magnetic field at the center of the disc is: