A charge q is moving with velocity ( vec v ) in the presence of both electric field \( \vec E \) and magnetic field \( \vec B \). If velocity (\( \vec v \)), electric field (\( \vec E \)) and the magnetic field (\( \vec B \)) are mutually perpendicular. The charge will pass through the field undeflected if:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( v=\displaystyle\frac{E}{B} \)
The charge goes straight only if the net force on it is zero. With \( \vec{v} \), \( \vec{E} \) and \( \vec{B} \) mutually perpendicular, the electric force \( qE \) and the magnetic force \( qvB \) act along the same line in opposite directions, so they must be equal in magnitude.
\( qE = qvB \Rightarrow v = \frac{E}{B} \)
The charge q cancels, so the condition does not depend on the charge or the mass of the particle.
Shortcut: Check the units. The unit of E is \( \mathrm{N\,C^{-1}} \) and of B is \( \mathrm{N\,A^{-1}\,m^{-1}} \), so \( E/B \) has the unit of speed, \( \mathrm{m\,s^{-1}} \). Option (2), \( B/E \), has the unit \( \mathrm{s\,m^{-1}} \), and Options (3) and (4) mix quantities with different units.
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), but it is still in the CUET 2026 syllabus, so do not skip it.
NCERT (Pre-rationalised edition, 2022-23):
Velocity Selector – “… Suppose, we adjust the value of E and B such that magnitude of the two forces are equal. Then, total force on the charge is zero and the charge will move in the fields undeflected. This happens when,
\( \displaystyle qE = qvB \quad \text{or} \quad v = \frac{E}{B} \qquad (4.7) \)”