An electron enters a crossed electrical and magnetic field region with a speed of \( 100\,\mathrm{m\,s^{-1}} \) along +x-axis and passes undeviated. The strength of magnetic field is 5.0 T and it acts along +z-axis. Give the electrical field in vector notations indicating its magnitude as well as direction:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \left(500\,\mathrm{V\,m^{-1}}\right)\hat{\jmath} \)
The electron passes undeviated when the electric force and the magnetic force on it cancel, which is the velocity selector condition:
\( q\vec{E} + q(\vec{v}\times\vec{B}) = 0 \Rightarrow \vec{E} = -\vec{v}\times\vec{B} \)
With \( \vec{v} = 100\,\hat{\imath}\,\mathrm{m\,s^{-1}} \) and \( \vec{B} = 5.0\,\hat{k}\,\mathrm{T} \), and \( \hat{\imath}\times\hat{k} = -\hat{\jmath} \):
\( \vec{v}\times\vec{B} = 100\times5.0\,(\hat{\imath}\times\hat{k}) = -500\,\hat{\jmath}\,\mathrm{V\,m^{-1}} \)
\( \vec{E} = -\vec{v}\times\vec{B} = +500\,\hat{\jmath}\,\mathrm{V\,m^{-1}} \)
The magnitude is \( E = vB = 100\times5.0 = 500\,\mathrm{V\,m^{-1}} \), directed along \( +y \).
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 – “… We shall consider the simple case in which electric and magnetic fields are perpendicular to each other and also perpendicular to the velocity of the particle, as shown in Fig. 4.7. … 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
\( \displaystyle qE = qvB \quad \text{or} \quad v = \frac{E}{B} \qquad (4.7) \)”