An electron (charge $q$ $coulomb$) enters a magnetic field of $H$ $weber/{m^2}$ with a velocity of $v\,m/s$ in the same direction as that of the field the force on the electron is

A proton (mass $ = 1.67 \times {10^{ – 27}}\,kg$ and charge $ = 1.6 \times {10^{ – 19}}\,C)$ enters perpendicular to a magnetic field of intensity $2$ $weber/{m^2}$ with a velocity $3.4 \times {10^7}\,m/\sec $. The acceleration of the proton should be

Two particles $\mathrm{X}$ and $\mathrm{Y}$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $\mathrm{X}$ and $\mathrm{Y}$ is :

A particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$ direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$ direction, extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is

What is Lorentz force ? Write an expression for it