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 largest value of force, Do not round intermediate calculation...

Do not round intermediate calculations; however for display purposes report intermediate steps rounded to four significant figures. Give your final answer(s) to three significant f

Material selection for de-oiling unit, • IGF Vessel SH: CS + 1.6 mm CA +...

• IGF Vessel SH: CS + 1.6 mm CA + Internal Coating Eductor: 304L SS or alternatively, 12Cr • ORF Vessel SH: CS + 1.6mm CA + Internal Coating Mixer: 316L SS • Skim Oil T

Explain the adiabatic system - thermodynamic, Explain the Adiabatic System ...

Explain the Adiabatic System - Thermodynamic Adiabatic System: A system along with adiabatic walls can just only exchange work and not heat with the surrounding is known as Adi

Generation of steam at constant pressure - thermodynamics, Generation of st...

Generation of steam at constant pressure: Steam is pure substance. Like any other pure substance it can also be converted into any of the three states, that is, solid, liquid

Clearance volume, Clearance Volume ( V C ) : The nominal volume of the c...

Clearance Volume ( V C ) : The nominal volume of the combustion chamber above the piston when it is at the top dead centre is the clearance volume. It is designated as V C an

Pin-jointed steel structure, Pin-jointed steel structure: Find out the...

Pin-jointed steel structure: Find out the forces in the members of the pin-jointed steel structure. Solution Joint D  Suppose f CD and f DE both as tensile forc

Resolving all of the forces normal to the inclined plane, Resolving all of ...

Resolving all of the forces normal to the inclined plane: A body weighing 500 N is resting on an inclined plane making an angle of 30 o with the horizontal. The coefficient o

Spot welding of different metals-stainless steel, Spot welding of different...

Spot welding of different metals-Stainless steel Stainless steel is having lower thermal conductivity compared to mild steel. Therefore, it requires less heat input. But, stain

Parallelograular law of forces and triangular of forces, two forces are act...

two forces are acting at a point''o'',determine magnitude and direction by using parallelogram law of forces and triangular law of forces

Common rules concerning corresponding option , COMMON RULES CONCERNING CORR...

COMMON RULES CONCERNING CORRESPONDING OPTION:     Let us consider the DATA DIVISION entries as shown below. Now, let us see which data items will be moved if

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