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

Thermodynamics, why constant volume line has more slop tha constant pressur...

why constant volume line has more slop tha constant pressure line in T-S diagram

Thrust and pressure, Thrust: The net force exerted by a liquid on any shie...

Thrust: The net force exerted by a liquid on any shield in contact with it, is called as thrust of liquid. Pressure:  The thrust operated by a liquid per unit area of the fie

Boilers, BOILERS: BOILERS : Boilers can be defined as closed pressu...

BOILERS: BOILERS : Boilers can be defined as closed pressure vessels that are used to generate steam at pressure much higher than atmospheric pressure by the transfer of he

Work-power-energy, Under the action of constant force, a 2kg block moves su...

Under the action of constant force, a 2kg block moves such that its position x as a function of time is given by X=t^3/3 ,where x in meters and t in sec , the workdone by force in

What do you know about series welds in spot welding, Q What do you know abo...

Q What do you know about Series welds in spot welding? It is a welding method in which two or more spots are produced simultaneously with only one common but indirect current p

Sada, Ask question #ccMinimum 100 words accepted#

Ask question #ccMinimum 100 words accepted#

Polymer, classification of polymers

classification of polymers

Compute minimum value of the horizontal force, Compute minimum value of the...

Compute minimum value of the horizontal force: Block A of weight 520N rest on horizontal top of block B having weight of 700N as shown in the figure given below. Block A

Sliding and rolling, Sliding and Rolling Consider the following example...

Sliding and Rolling Consider the following example. A cylinder of mass  M  and radius  R  is held at rest on a plane inclined at an angle to    to the horizontal. When the cyl

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