Two long straight parallel wires are a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field $B$ along the line $xx'$ is given by:

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

$A$ rectangular coil carrying current is placed in a non-uniform magnetic field. On that coil, the total:

The neutral temperature of a thermocouple is $350\,^{\circ}C$ when the cold junction is at $0\,^{\circ}C$. When the cold junction is immersed in a bath of $30\,^{\circ}C$,the inversion temperature is .............. $^{\circ}C$.

Three infinite wires are arranged in space in three dimensions (along $x$,$y$,and $z$ axes) as shown. Each wire carries current $i$. Find the magnetic field at point $A$ located at $(r, -r, 0)$.

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.