The ratio of time periods of $\alpha$-particle and proton moving on circular path in a uniform magnetic field is . . . . . . .

$A$ stream of electrons and protons are directed towards a narrow slit in a screen (see figure). The intervening region has a uniform electric field $E$ (vertically downwards) and a uniform magnetic field $B$ (out of the plane of the figure) as shown. Then:

$A$ particle having the same charge as an electron moves in a circular path of radius $0.5 \, cm$ under the influence of a magnetic field of $0.5 \, T$. If an electric field of $100 \, V/m$ makes it move in a straight path,then the mass of the particle is (given charge of electron $= 1.6 \times 10^{-19} \, C$):

Work done by a magnetic field of $1\,T$ on a particle of charge $1\,C$ moving with a speed of $5\,m/s$ in one second is........$J$.

An electrically charged particle enters a uniform magnetic field in a direction perpendicular to the field with a velocity $v$. Then,it travels:

$A$ proton is moving along the $Z$-axis in a magnetic field. The magnetic field is along the $X$-axis. The proton will experience a force along