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

High carbon tool steels, High Carbon Tool Steels Tools are implements...

High Carbon Tool Steels Tools are implements such are employed to shape, cut or deform other materials. They are largely made in steel, although other alloys have also been i

Explain about corrosion rates, Q. Explain about Corrosion Rates? Corros...

Q. Explain about Corrosion Rates? Corrosion rates of Corrosion data presented in these standards are in graphical form. The corrosion curves for the majority of the metals

Couple, What are properties of couple

What are properties of couple

Need of a spectrophotometer, Need of a spectrophotometer: The specific...

Need of a spectrophotometer: The specific instructions will differ with other models, but the principles remain. 1. The instrument must have been warm for at least 15 min.

Stress analysis, what is the importance of stress analysis in steels

what is the importance of stress analysis in steels

Difficulties with motion sickness, In designing rotating space stations to ...

In designing rotating space stations to give for artificial-gravity environments, one of the constraints that must be considered is motion sickness. Studies have shown that the neg

Describe loose piece pattern, Loose piece pattern This type of pattern ...

Loose piece pattern This type of pattern is also used when the contour of the part is such that withdrawing the pattern from the mould is not possible. Hence during moulding th

Illustrate the future trends in automobile, Short answer Type. a) Writ...

Short answer Type. a) Write the difference Between Dry clutch and Wet ? b) What is difference Between Chasis and Frame? c) Illustrate the Future trends in Automobile

Crankshaft design, i have designed a crankshaft for 3 cylinder engine i wan...

i have designed a crankshaft for 3 cylinder engine i want to know how to balance it

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