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

Explain concept of reaming of radial drilling machine, Explain concept of R...

Explain concept of Reaming and boring of radial drilling machine Reaming Reaming is accurate way of sizing and finishing the pre-existing hole. Multi tooth cutting tool. A

Area Moment of Inertia, Are a Moment of Inertia Moment of force about ...

Are a Moment of Inertia Moment of force about a point is product of the force ( F ) and perpendicular distance ( d ) between point and line of action of that is F.d. This mome

determine the minimum cross section area of graph, To design a cantilevere...

To design a cantilevered truss to support the loads shown in the figures, two layouts are proposed as shown in Figs. A and B. All truss members are steel with allowable stress of 2

Define advantage and disadvantage of electron beam machining, Define Advant...

Define Advantage and Disadvantage of Electron Beam Machining Advantage  1. Suitable for automatic machining. 2. Absence of mechanical contact between work piece and too

Supports for rigid bodies, Supports for Rigid Bodies: In this unit, yo...

Supports for Rigid Bodies: In this unit, you have learnt to classify various types of supports and constraints, rollers, rockers, ball and socket joints, cables, short links,

CAPP, Applications of capp

Applications of capp

Law of Parallelogram of Forces, To finding ? in Law of parallelogarm forces...

To finding ? in Law of parallelogarm forces We take Q sina(Along Vertical Side) & Q cosa(Along Horizontal Side) I didn''t get that point Q sina & Q cosa how it derived? Can you

Show the welding processes and restrictions, Q. Show the Welding Processes ...

Q. Show the Welding Processes and Restrictions? Welding may be performed manually, semi-automatically and or automatically using any process or combination of processes accepte

Orthogonal cutting test, In an orthogonal cutting test with a tool of rake ...

In an orthogonal cutting test with a tool of rake angle 10 degree , the following observations were made. 20 Chip thickness ratio = 0.3 Width of cut = 6mm Uncut chip thicknes

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