Uniform alternate electric field, Mechanical Engineering

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

Posted Date: 9/18/2012 1:06:00 AM | Location : United States







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

Write discussion on Uniform alternate electric field
Your posts are moderated
Related Questions
Explain the Disadvantages of Automation? a) Initial cost is higher providing additional features in machine tools. b) Skilled personnel's are required for maintenance of aut

Arc Spot Welding In this process, coalescence at the overlapping surfaces is produced in one spot by heating with an electric arc between an electrode and the work. The weld i

If Excessive Pedal Pressure Required Causes of Problem Remedy Incorrect shoe placement Improper anchor pin position l


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

I have a bevel gear and shaft and I want to know the maximum load that can be applied on it. also I have no information about it, what kind of information is needed for this calcul



Moment of Force: Defin e Moment of Force? Describe moment center and moment arm. Also classify the moment. Sol.: It is turning effect produced by force, on the body, on wh

Insulators Thermal insulators are essential in industrial practices, domestic and equipment appliances. That type of materials is basically those that do not have free electro