Uniform alternate electric field, Mechanical Engineering

Assignment Help:

Uniform Alternate Electric Field

Suppose a particle moves under a uniform (i.e. independent of space co-ordinates) but alternating electric field E given by,


E = E0 sin ω t = ( E0 i) sin ω t                                     (i)

where, E0 is amplitude and ω is angular frequency of oscillation. We define the direction of electric field as X-axis.

The equation of motion of the particle of mass m and charge q in this field is,

1832_download (1).png 

Integrating, we find

 476_download.png 

where constant of integration c1 is set by initial condition: at t = 0, when E = 0, let v = v0. Hence, we get

915_download (2).png 

Integrating once again, we find

 129_download (3).png 

where constant of integration r0 is the initial position of the particle; at t = 0r = r0.

We can always put r0 = 0; let us also take v0 = 0. Further, if E0 = E0 i, we have

1481_download (4).png 

The particle moves along X-axis with time dependent speed vx (t). The average speed of the particle during a cycle is,

912_download (5).png 

vx is called the drift velocity of the particle. The displacement of the particle during one complete cycle, i.e. in time T,

803_download (6).png 

The graph between x and t is obtained by superposing the sine curve and the straight line,

x = x1 + x2

2155_download (7).png 

If v0 ≠ 0, the particle may continue to move along y and z directions with constant initial velocities voy and voz. Simultaneously, it is drifted towards X-axis by a fixed distance per cycle, viz.

611_download (8).png


Related Discussions:- Uniform alternate electric field

Tolerances, difference between geometric and amnufacturing tolerances

difference between geometric and amnufacturing tolerances

Define cases in which automation is done, Define Cases in which Automation ...

Define Cases in which Automation is Done Automation is done in following cases:- a) Loading and unloading of parts. b) Automatic production lines. c) Automatic tool ch

Explain the semi-automatic extension of screw conveyor, Explain the Semi-Au...

Explain the Semi-Automatic Extension of screw conveyor "Semi-Automatic Extension of screw conveyor as per the screed width by telescopic-tube" Procedure: The extension of

Vitrification-manufacturing methods of ceramics, Vitrification This is...

Vitrification This is liquid phase sintering. It is achieved via incorporating a component that melts to viscous liquid during sintering. Such viscous liquid solidifies in gla

Planning a retail interior space, Question 1: A good display of the mer...

Question 1: A good display of the merchandise is the result of planning, cooperation and coordinating. A good schedule of work is important for a good design with the use of me

Micrometer or screw gauge-measuring tools , Micrometer (or Screw Gauge): T...

Micrometer (or Screw Gauge): There are two different types of micrometers - inside and outside micrometers. A micrometer also has two scales - Main scale and Vernier scale (Figure

Deflection at the centre - maximum deflection, Deflection at the centre - m...

Deflection at the centre - maximum deflection: A simply supported beam of span 6 m is subjected to Udl of 24 kN/m for a length of 2 m from left support. Discover the deflectio

Chemistry, what desaster made chemistry

what desaster made chemistry

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd