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

Evaluate the actual over all efficiency of the turbine, (a) An engine uses ...

(a) An engine uses 6.5 Kg of oil per hr of a calorific value 30,000 kJ / kg. If the B. P. of the engine is 22KW and mechanical efficiency 85%. Calculate (i) Brake thermal eff

Stitch welding, Stitch welding Here, a series of overlapping spot welds...

Stitch welding Here, a series of overlapping spot welds are made with the spot welding machine using the conventional electrode tip. Both water tight and gas tight joints can b

Cooling period of furnace pipe, We shutdown our furnace and always encounte...

We shutdown our furnace and always encountered crack on our piping at the weld joints. I investigated that upon shutdown the furnace cracking, our maintenance immediately remove th

Motion of two bodies - smooth surface and smooth pulley, Motion of two bodi...

Motion of two bodies - Smooth surface and smooth pulley: THE HORIZONTAL SURFACE IS SMOOTH AND STRING IS PASSING OVER SMOOTH PULLEY: Figure shows two weights W 1 and W 2 c

Capp for machining process, CAPP for Machining Process This explained ...

CAPP for Machining Process This explained mainly two different approaches to Computer Aided Process Planning, i.e.  (a) Variant approach, and  (b) Generative approach.

Belt friction, Ask question # how to derive a expression for the centifugal...

Ask question # how to derive a expression for the centifugal tension in belt driver

Determine strain using wheatstone bridge, a) Can you explain Discuss LVDI i...

a) Can you explain Discuss LVDI in detail. b) Derive the expression for calculating strain using wheatstone bridge. c) Distinguish between analog and digital transducers.

Ceramics, Ceramics Ceramics are mostly inorganic crystalline materials...

Ceramics Ceramics are mostly inorganic crystalline materials characterized by high melting point and low ductility. Such materials are processed via methods other than melting

Find out the horizontal and vertical components of the force, Find out the ...

Find out the horizontal and vertical components of the force: A force of 120 N is exerted on a hook in the ceiling as illustrated in Figure. Find out the horizontal and vertic

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