$A$ helium nucleus makes a full rotation in a circle of radius $0.8 \ m$ in $2 \ s$. The value of the magnetic field $B$ at the centre of the circle will be

The Earth's magnetic field at a given point is $0.5 \times 10^{-5} \, Wb/m^2$. This field is to be annulled by the magnetic induction at the center of a circular conducting loop of radius $5.0 \, cm$. The current required to be flown in the loop is nearly......$A$

Write the proportionality constant of the Biot-Savart law with its unit and value (magnitude).

$A$ current passing through a circular coil of two turns produces a magnetic field $B$ at its centre. The coil is then rewound so as to have four turns and the same current is passed through it. The magnetic field at its centre now is

The ratio of the magnetic field at the centre of a current-carrying coil of radius $r$ to the magnetic field at a distance $r$ from the centre of the coil on its axis is $\sqrt{x}: 1$. The value of $x$ is $............$

$A$ circular loop of radius $r$ is carrying current $I \ A$. The ratio of the magnetic field at the centre of the circular loop to the magnetic field at a distance $r$ from the centre of the loop on its axis is: