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

Left side view of a motorcycle parts of motorcycle, Figure : Left Side View...

Figure : Left Side View of a Motorcycle Part No. Name Functions 1 Fuel cock Used to open or close the

Working of steam engine , Working of stream engine: The high pressure ...

Working of stream engine: The high pressure steam from boiler is supplied to the steam chest. The high pressure steam enters cylinder through inlet port and exerts pressure on

Blasting abrasive, Blasting Abrasive: Sand had been use widely before ...

Blasting Abrasive: Sand had been use widely before new abrasive media invented. Today, manufacturer had more choices and better options in choosing blasting media for their ow

Petrol-general safety tips , Petrol: Work in a well-ventilated area. Keep ...

Petrol: Work in a well-ventilated area. Keep flames or sparks away from the work area or where petrol is stored.

Characterised punching shear failure in bearing capacity, How can punching ...

How can punching shear failure are characterised in bearing capacity? Punching Shear Failure This mode of failure is characterised by large deformations beneath the footing

Calculate sif of crack - beam, Calculate sif of crack - beam: An edge ...

Calculate sif of crack - beam: An edge cracked beam carries crack in its central plane whose lengths is 5 mm. A load of 1000 N is applied opposite to crack so that crack would

Rockwell hardness test, Rockwel l Hardness Test: The specimen is subj...

Rockwel l Hardness Test: The specimen is subjected to a major load for about 15 seconds after the initial load. ASTM says 13 scales for testing of wide range of materials. Th

Dynamic magnifier-forced vibration-synchronous whirl, Dynamic Magnifier: ...

Dynamic Magnifier: This is function of frequency ratio. Forced Vibration: While the system is continuously excited by an external force or internally produced force, the v

Weld preparation-joint tolerance-cleaning, WELD PREPARATION: Joint Toleranc...

WELD PREPARATION: Joint Tolerance & Cleaning   Joint Tolerance The allowable tolerance of joint dimensions depends upon whether the welding is to be done manually or

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