The ratio of the magnetic field at the centre of a current carrying coil of the radius $a$ and at a distance ‘$a$’ from centre of the coil and perpendicular to the axis of coil is

Two concentric coplanar circular loops of radii ${r_1}$ and ${r_2}$ carry currents of respectively ${i_1}$ and ${i_2}$ in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the centre of the loops is half that due to ${i_1}$ alone at the centre. If ${r_2} = 2{r_1}.$ the value of ${I_2}/{I_1}$ is....

In a region of space, a uniform magnetic field $B$ exists in the $y-$direction.Aproton is fired from the origin, with its initial velocity $v$ making a small angle $\alpha$ with the $y-$ direction in the $yz$ plane. In the subsequent motion of the proton,

A straight wire of diameter $0.5\, mm$ carrying a current of $1\, A$ is replaced by another wire of $1\, mm$ diameter carrying the same current. The strength of magnetic field far away is

A thin rod is bent in the shape of a small circle of radius $'r'$. If the charge per unit length of the rod is $'\sigma ',$ and if the circle is rotated about its axis at the rate of $'n'$ rotation per second, the magnetic induction at a point on the axis at a large distance $'y'$ from the centre is

Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is