Transverse electric field, Mechanical Engineering

Transverse Electric Field

Consider a charged particle (e.g. an electron) moving along X-axis with constant velocity v, i. At x = 0, it enters into a region where a uniform constant electric field E exists along Y-axis, i.e. for x > 0Ey jEx = Ez = 0. This electric field applies a forceq E along the Y-axis, i.e. for x > 0E = Ey jEx = Ez = 0. This electric field applies a force q E along the Y-axis, while particle continues to move along X-axis with constant initial velocity vx i. Such a case is realized in laboratory by passing a beam of electrons between the plates of a parallel plate capacitor, as in cathode ray tube (CRT).


The electric field applies a constant force, qEy, on the particle along Y-axis. Hence,

1850_download.png 

which gives vy = ay ty = ½ ay r2                       (ii)

where ay = qEy/m ; y and vy at t = 0 are zero. In the same time t, particle moves a distance x along x along X-axis with constant initial velocity vx i, so that

x = vx t                                                              (iii)

Eliminating t, we find the trajectory of the particle:

2385_download (1).png 

which is equation of a parabola. This is analogous to parabolic motion of a projectile which moves horizontally with constant a velocity and vertically under constant acceleration g.

If the particle remains in the remains in the field only between x = 0 to x = l (e.g. l may be length of capacitor plates in CRT), then the deflection of particle along Y-axis, as it comes out at x = l, is

1226_download (2).png 

At x = l, particle velocity v is given by

1952_download (3).png 

which makes an angle θ with the X-axis, where

192_download (4).png 

50_download (5).png 

Since the displacement on screen is proportional to electric field, the position of the beam on screen tells about the value of (an unknown) electric field (or potential) which may be applied across the capacitor plates. 

Posted Date: 9/18/2012 1:18:20 AM | Location : United States







Related Discussions:- Transverse electric field, Assignment Help, Ask Question on Transverse electric field, Get Answer, Expert's Help, Transverse electric field Discussions

Write discussion on Transverse electric field
Your posts are moderated
Related Questions
Determine net work done: 5 m 3   of air at 2bar, 27 0 C is compressed to 6bar pressure following PV 1. 3   = constant. It is expanded subsequently adiabaticall


Find out extension: Q: A bar having length 25mm has varying cross section. It carries load of 14KN. Find out extension if cross section is given by (6 + x 2 /100) mm 2

Q. Determine the Bolt Torque? The value of the bolt torque, which will give the desired bolt stress, can be calculated from Equation. The friction coefficient (K) is for a well

In mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the

what is magnetostriction?

A load cell based on a simply-supported beam with rectangular cross-section is shown below. The beam is made using a tool steel alloy with E = 200 GPa, ν = 0.285. Two strain gages

Replace the two parallel forces by single force: Replace the two parallel forces acting on the control lever by a single equivalent force R.   Sol.: Since single equ

Write brief notes on the following : (a) Draught System (b) Binary Vapour Cycle (c) Cooling Towers (d) Governing of steam turbines

Q. Use of high temperature material Flare Tips? A variety of high temperature alloys (typically stainless steels and/or nickel-base alloys) are employed in the construction of