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

Determine the smallest increment of strain hat, A 16-bit A/D board is arran...

A 16-bit A/D board is arranged to accept voltage signals ranging from -5V to +5V.  The A/D board is used to monitor the output from the Wheatstone bridge shown below.  The strain g

CAE & modelling, when is scaling transformation termed as linear

when is scaling transformation termed as linear

Advantages of multiple vessels, Reduced costs result from failure Easier...

Reduced costs result from failure Easier fermenter planning (particularly in light of above) Easier downstream scheduling Off the shelf supplies e.g. motors Routine sup

EM2013KEN2401MECH, Hi. I have made a payment for the above ticket number. W...

Hi. I have made a payment for the above ticket number. Will I get all the workings out too? [email protected]

Find out the intensity of the external pressure, Find out the intensity of ...

Find out the intensity of the external pressure: A thick cylinder of 0.5 m external diameter & 0.4 m internal diameter is subjected simultaneously to internal & external press

Velocity diagram, how do I learn how to present velocity and acceleratio...

how do I learn how to present velocity and acceleration diagram from a free space diagram

Numerical problems based on the cantilever beam, Numerical Problems Based o...

Numerical Problems Based on the Cantilever Beam: Draw the SF and BM diagram for the beam as shown in the figure given below. Also indicate principal values on diagrams.

Determine maximum internal diameter of hollow shaft, Determine maximum inte...

Determine maximum internal diameter of hollow shaft: A solid shaft of mild steel which is 200 mm in diameter is to be replaced by hollow shaft of alloy steel for which the al

Question.., Two concentric perforared plates are seperated by a 200mm laund...

Two concentric perforared plates are seperated by a 200mm launder and form the flow exit for a clarifier (figure 1). The inlet water flow of 1200 mcubed/hour into the clarifier is

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