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

Desing, what is the maximum principle stress

what is the maximum principle stress

How are the refrigerants classified, How are the refrigerants classified? D...

How are the refrigerants classified? Describe the desirable property of a good refrigerant. Explain in brief the thermodynamics, safe and physical working property of an ideal r

Evaluation of specific volume of steam - thermodynamics , Evaluation of Spe...

Evaluation of Specific Volume of Steam: Specific volume of steam means the volume which is occupied by unit mass of steam. It is expressed in m3 /kg. Specific volume of steam

What is transmission system and what do you mean by a gear?, (a) What is tr...

(a) What is transmission system? Represent the main components of transmission system with the help of diagram. (b) What do you mean by terms torque, power and RPM? (c) What

Stress strain curves for the brittle materials, Stress strain curves for th...

Stress strain curves for the brittle materials: Stress strain curves for the brittle materials : Materials which show small elongation before they fracture are called as br

Determine the elongation of plate, Determine the elongation of plate: ...

Determine the elongation of plate: Q: A steel bar AB which is having uniform thickness 2 cm, tapers from 1.5 cm to 7.5 cm uniformly in a length of 50 cm. From 1 st principle

Can you use motor oil in a hydraulic system, Hydraulic fluid has to pass a ...

Hydraulic fluid has to pass a dissimilar set of standards than motor oil. Motor oil has tackifiers, lower sulfur content, and other ingredients that could solve harmful to the seal

Concept of continuum - thermodynamics, Concept of continuum - thermodynamic...

Concept of continuum - thermodynamics: Sol: Even the simplification of matter into molecules, atoms, electrons, etc. is too complex a picture for many problems of thermodyna

Machin of dynamics, Ask question Prove maximum fluctuation of energy ?E=2EC...

Ask question Prove maximum fluctuation of energy ?E=2ECS.

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