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

Connecting rod-basic components of engine , Connecting Rod : It connects t...

Connecting Rod : It connects the piston and the crankshaft and transmits the power from the piston to the crankshaft. It has a small end (through which gudgeon pin passes to conne

Explain interference between two mating gears, What do you understand by in...

What do you understand by interference between two mating gears ? if interference between two involutes gears is to be avoided then show that the maximum length of arc of contact w

Wind induced vibration of vertical vessels, Q. Wind Induced Vibration of Ve...

Q. Wind Induced Vibration of Vertical Vessels? Vertical vessels having a height-to-diameter ratio (h/D) (does not include insulation thickness but does include skirt height) gr

Classification of welding based on mode of energy transfer , Classification...

Classification of welding Based on Mode of Energy Transfer Energy is converted from one form to another. Any form of energy can be converted to heat energy, which can be used f

Calculate the magnitude and position of the balance mass, The four masses m...

The four masses m1, m2, m3 and m4 having their radii of rotation as 200mm, 250mm, 150mm, 250mm and 300mm are 200kg, 300kg,240kg and 260kg in magnitude respectively. The angles betw

Determine the location of the hydraulic jump, A rectangular channel of widt...

A rectangular channel of width 12ft has an upstream slope of 0.02ft/ft and a downstream slope of 0.0005 ft/ft. Both reaches have lengths of 500 ft. The upstream reach has a Manning

Evaluate force and moment - mechanics, Evaluate force and moment: Wha...

Evaluate force and moment: What force and moment is transmitted to supporting wall at A   A force of 15 KN is transmitted to wall along with anticlockwise mome

Furances, type of furances and disadvantage advantage

type of furances and disadvantage advantage

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