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

Electrodes- hardfacing electrodes, Hardfacing Electrodes There are many...

Hardfacing Electrodes There are many types of hard facing electrodes. These electrodes are mainly useful in the maintenance and repair of machinery parts and equipments subject

Illustrates about the need for reinforcement, Illustrates about the need fo...

Illustrates about the need for reinforcement? NEED FOR REINFORCEMENT Concrete is economical and durable and is currently universally utilized for footings. Plain concrete is

example of alteration of position and reference line method, Example of Al...

Example of Alteration of Position and Reference Line Method: Sketch the projections of a pentagonal prism edge of the base 50 millimeter long and height 90 millimeter, the axi

Explain the protocol for stress testing, Q. Explain the protocol for stress...

Q. Explain the protocol for stress testing? The protocol for stress testing should be structured to include the following: 1) Continuous ECG monitoring. 2) Hard copy ECG

Briefly explain model scale design, Q. Briefly explain Model scale design? ...

Q. Briefly explain Model scale design? Knowledge of dynamic similarity conditions enables evaluation of model scales. Almost alI the problems related to river hydraulics are ab

Composites , For an automotive component of your choice that is traditional...

For an automotive component of your choice that is traditionally metallic, review how it could be re-engineered as a composite? How factors such as fibre & matrix type, fibre volum

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