Velocity Selector

A velocity selector exploits the fact that the electric force $qE$ and the magnetic force $qvB$ act in opposite directions on a moving charge when the fields are mutually perpendicular and oriented appropriately. Only particles for which these forces exactly cancel pass straight through, so the selection condition is $qE=qvB$, independent of charge and mass. Solving for speed gives $v=\frac{E}{B}=\frac{3\times 10^4}{0.6}=5\times 10^4{\text{m s}}^{-1}$. The option $1.8\times 10^4{\text{m s}}^{-1}$ wrongly multiplies $E$ by $B$ instead of dividing. The option $2\times 10^5{\text{m s}}^{-1}$ inverts the ratio, using $B/E$ scaled wrongly. The option $5\times 10^5{\text{m s}}^{-1}$ misplaces a power of ten. This crossed-field configuration is the basis of the velocity selector that feeds mass spectrometers, as treated in NCERT and J. J. Thomson's experiment. A unit check confirms volt per metre divided by tesla yields metre per second, and the result is a physically reasonable beam speed. Because the selection condition is independent of charge and mass, the velocity selector delivers a beam in which every particle shares one common speed, regardless of how the particles were produced. This makes it the essential first stage before a mass spectrometer, where the cleanly monoenergetic beam then enters a pure magnetic field and separates by mass. Historically the same crossed-field arrangement let Thomson measure the charge-to-mass ratio of the electron.