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

Engineering drawing, in orthographic projection why in quadrant is taken in...

in orthographic projection why in quadrant is taken in anticlock wise

Plate clutch pressure height-clutch slipping, Plate clutch pressure height ...

Plate clutch pressure height : Check plate clutch pressure leg height by placing the plate clutch pressure on the surface plate. Plate clutch pressure should not tilt on the surfa

What are the various types of wear found in cutting tool, What are the cond...

What are the condition that could allow a continuous chip to be formed in a metal cutting ? How is metal removed in metal cutting? Illustrate the Process with neat sketch. What

Determine the point of intersection jets, A tank has two identical orifices...

A tank has two identical orifices in one of its vertical sides. The upper orifice is 3m below the water surface and lower one is 5m below the water surface. If the value of Cv for

Disc type brake, Disc Type Brake:  As shown in Figure the disc brake ...

Disc Type Brake:  As shown in Figure the disc brake consists of a pearlitic grey cast iron disc bolted to the wheel hub and a stationary housing called caliper. Casting in tw

Illustrate dynamically equivalent system, Illustrate with required expressi...

Illustrate with required expression for dynamically equivalent system. Illustrate in detail about the Balancing of Radial Engines.

Evaluate force by replacing equivalent force, Evaluate force by replacing e...

Evaluate force by replacing equivalent force: In designing lifting hook, the forces acting on horizontal section through B can be determined by replacing F by equivale

Displacement or swept volume, Displacement or Swept Volume ( V s ) : The ...

Displacement or Swept Volume ( V s ) : The nominal volume swept by the working piston when travelling from one dead centre to the other is called the displacement volume. It is e

Steam generator load balancing, Q. Steam Generator Load Balancing? The ...

Q. Steam Generator Load Balancing? The pressure controller output is cascaded to individual stations, one for each boiler. These allow selective increase or decrease of the du

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