$A$ loop of irregular shape made of flexible conducting wire carrying a clockwise current is placed in a uniform inward magnetic field,such that its plane is perpendicular to the field. Then the loop:

$A$ charged 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 the figure. Which of the 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.

Answer the following questions:
$(a)$ $A$ magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. $A$ charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ $A$ charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction,and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.

Current flows through uniform,square frames as shown. In which case is the magnetic field at the centre of the frame not zero?

Two parallel long wires carry currents $i_1$ and $i_2$ with $i_1 > i_2$. When the currents are in the same direction,the magnetic field midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,it becomes $40 \, \mu T$. The ratio $i_1/i_2$ is

$A$ metal sample carrying a current along $X-$ axis with density $J_x$ is subjected to a magnetic field $B_z$ (along $z-$ axis). The electric field $E_y$ developed along $Y-$ axis is directly proportional to $J_x$ as well as $B_z$. The constant of proportionality has $SI$ unit: