An electric current is flowing through a circular coil of radius $R$ . The ratio of the magnetic field at the centre of the coil and that at a distance $2\sqrt 2 \,R$ from the centre of the coil and on its axis is

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ?

Acharged particle enters a uniform magnetic field perpendicular to its initial direction travelling in air. The path of the particle is seen to follow the path in figure. Which of statements $1-3$ is/are correct?

$[1]$ The magnetic field strength may have been increased while the particle was travelling in air

$[2]$ The particle lost energy by ionising the air

$[3]$ The particle lost charge by ionising the air

Unit of magnetic permeability is

A charge $Q$ is uniformly distributed over the surface of nonconducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field ofinduction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure

Which of the following gives the value of magnetic field according to, Biot-Savart’s law’