An arrangement with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown in the figure. The permeability of free space is $\mu_0$. The magnetic field at $C$ is

Three infinite wires are arranged in space in three dimensions.(along $x, y$ and $z$ axis) as shown. Each wire carries current $i$ . Find magnetic field at $A$ 

Two concentric coils each of radius equal to $2\pi \,{\rm{ }}cm$ are placed at right angles to each other. $3$ $ampere$ and $4$ $ampere$ are the currents flowing in each coil respectively. The magnetic induction in $Weber/{m^2}$ at the centre of the coils will be $({\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A.m)$

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

Find the magnitude of magnetic field at point $p$ due to a semi - infinite wire given below

Magnetic field due to $0.1\, A$ current flowing through a circular coil of radius $0.1\, m$ and $1000$ $turns$ at the centre of the coil is