Velocity selector by setting the voltage. A particle of charge -Q and mass m gets shot rightwardat initial speed vo between the two plates of a parallel-plate capacitor. The plates are fixed a distanced apart and have length L. The particle enters the capacitor midway between the plates, a distanced/2 from either one. A uniform magnetic field of strength Bo points into the page. This field existsonly between the plates. Initially the capacitor is not charged.d.L(a) The particle deflects and crashes into one of the plates. Does it hit the upper plate or the lowerplate? How far from the left end of the plate does it crash?(b) Now the capacitor is connected to a power supply. To what voltage should the power supply beset so that the particle travels in a straight line while between the plates? Which plate should beconnected to the positive terminal of the power supply?(c) Now suppose you dial down the voltage on the supply just a tiny bit below what you found in part(b). Sketch the particle's trajectory, including after it leaves the space between the two plates.

Answered: Velocity selector by setting the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Velocity selector by setting the voltage. A particle of charge -Q and mass m gets shot rightward
at initial speed vo between the two plates of a parallel-plate capacitor. The plates are fixed a distance
d apart and have length L. The particle enters the capacitor midway between the plates, a distance
d/2 from either one. A uniform magnetic field of strength Bo points into the page. This field exists
only between the plates. Initially the capacitor is not charged.
d.
L
(a) The particle deflects and crashes into one of the plates. Does it hit the upper plate or the lower
plate? How far from the left end of the plate does it crash?
(b) Now the capacitor is connected to a power supply. To what voltage should the power supply be
set so that the particle travels in a straight line while between the plates? Which plate should be
connected to the positive terminal of the power supply?
(c) Now suppose you dial down the voltage on the supply just a tiny bit below what you found in part
(b). Sketch the particle's trajectory, including after it leaves the space between the two plates.

Expert Solution

Step 1

a) The parallel deflects and crashes into one of the plates as the charge is negative. So it will hit the lower plate.

The distance from the left end is as follows:

$r = \frac{m V_{O}}{B_{0} Q}$

Therefore the particle will follow a circular path and makes one-quarter of the circle before hitting the plate. So distance r will be the radius of the circular path.

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