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
Similar Questions
A magnetic field
A magnetic field
The figure shows three situations when an electron with velocity $\vec v$ travels through a nuniform magnetic field $\vec B$ . In each case, what is the direction of magnetic force on the electron?
The figure shows three situations when an electron with velocity $\vec v$ travels through a nuniform magnetic field $\vec B$ . In each case, what is the direction of magnetic force on the electron?
A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20\;V{m^{ - 1}}$ and $0.5 T$ at right angles to the direction of motion of the electrons. What is the velocity of the electrons............ $m{s^{ - 1}}$
A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20\;V{m^{ - 1}}$ and $0.5 T$ at right angles to the direction of motion of the electrons. What is the velocity of the electrons............ $m{s^{ - 1}}$
- [AIPMT 1996]
Two particles of charges $+Q$ and $-Q$ are projected from the same point with a velocity $v$ in a region of uniform magnetic field $B$ such that the velocity vector makes an angle $q$ with the magnetic field. Their masses are $M$ and $2M,$ respectively. Then, they will meet again for the first time at a point whose distance from the point of projection is
Two particles of charges $+Q$ and $-Q$ are projected from the same point with a velocity $v$ in a region of uniform magnetic field $B$ such that the velocity vector makes an angle $q$ with the magnetic field. Their masses are $M$ and $2M,$ respectively. Then, they will meet again for the first time at a point whose distance from the point of projection is
A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. the radius of the circular portion of the path is :-
A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. the radius of the circular portion of the path is :-