A rectangular region of dimensions ( $\omega \times l(\omega) \ll l$ ) has a constant magnetic field into the plane of the paper as shown in the figure below. On one side, the region is bounded by a screen. On the other side, positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V < 0$ and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen?
A rectangular region of dimensions ( $\omega \times l(\omega) \ll l$ ) has a constant magnetic field into the plane of the paper as shown in the figure below. On one side, the region is bounded by a screen. On the other side, positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V < 0$ and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen?
- [KVPY 2017]
- A
Ions with $q > \frac{2 V m}{B^{2} \omega^{2}}$ will hit the screen
- B
Ions with $q < \frac{2 V m}{B^{2} \omega^{2}}$ will hit the screen
- C
All ions will hit the screen
- D
Only ions with $q=\frac{2 V m}{B^{2} \omega^{2}}$ will hit the screen
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- [AIEEE 2012]
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- [AIEEE 2005]
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- [JEE MAIN 2020]