Electrons moving with different speeds enter a uniform magnetic field in a direction perpendicular to the field. They will move along circular paths.

An electron is moving along the positive $x$-axis. To make it move in an anticlockwise circular path in the $x-y$ plane,a magnetic field must be applied:

Two identical charged particles enter a uniform magnetic field with the same speed but at angles $30^{\circ}$ and $60^{\circ}$ with the field. Let $a, b,$ and $c$ be the ratios of their time periods,radii,and pitches of the helical paths,respectively. Then:

$A$ charge of $2.0\,\mu C$ moves with a speed of $3.0 \times 10^6\,m/s$ along the positive $X$-axis. $A$ magnetic field of strength $\vec B = -0.2\,\hat k\,T$ exists in space. What is the magnetic force $(\vec F_m)$ on the charge?

$A$ $2 \, MeV$ proton is moving perpendicular to a uniform magnetic field of $2.5 \, T$. The force on the proton is

An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns per unit length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid,the maximum possible value of $v$ is (all symbols have their standard meaning):