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.

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.

$A.$ The electron will experience magnetic force along the axis of the solenoid.

$B.$ The electron will not experience magnetic force.

$C.$ The electron will continue to move along the axis of the solenoid.

$D.$ The electron will be accelerated along the axis of the solenoid.

$E.$ The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_{d}$ and $r_{p}$ are the radii of their circular paths respectively, then the ratio $\frac{r_{d}}{r_{p}}$ will be $\sqrt{ x }: 1$ where $x$ is ……….

Write equation of Lorentz force.

A metallic block carrying current $I$ is subjected to a uniform magnetic induction $\overrightarrow B $ as shown in the figure. The moving charges experience a force $\overrightarrow F $ given by ……….. which results in the lowering of the potential of the face …….. Assume the speed of the carriers to be $v$