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

Fluid Question, If water is pumped from a pristine stream and piped to a st...

If water is pumped from a pristine stream and piped to a storage tank installed on a tower above the facility, a) What is the minimum dimension for "X" to achieve the required pres

Define heat for electrical resistance welding, Q. Define Heat for electrica...

Q. Define Heat for electrical resistance welding? The heat, H for electrical resistance welding is generated by passing a large electrical current ( of the order of 3000 to 100

Determine the location of the hydraulic jumps - water depths, Problem: In H...

Problem: In HEC-RAS, model this system as 1 reach with cross-sections every 2 ft. For all 3 discharges (labeled as: design, low, flood), (a) Determine the water depths 10 ft fro

Ideal fluids in motion, In hydrostatic we consider that fluids were at rest...

In hydrostatic we consider that fluids were at rest. Now we relax this consideration but with caution. We will discuss the flow of an real fluid. There are the assumptions about pe

Wire melting characteristics, WIRE MELTING CHARACTERISTICS A non linear r...

WIRE MELTING CHARACTERISTICS A non linear relationship exists between the rate at which the wire is fed into the arc and the current required to burn it off to maintain a constan

What is the problem in paving material distribution system, What is the pro...

What is the problem in Paving material distribution system James H. Bassett found the problem in Paving material distribution system In particular, separation of the larger agg

Rankine cycle, A cycle stream power plant is to be designed for stream temp...

A cycle stream power plant is to be designed for stream temperature and turbine 350

GD & T Expert needed to drawing chenck, Dou you have someone with good GD &...

Dou you have someone with good GD & T knowledge who can help me with ceheck, markup and comment mechanical drawings in PDF file format wich I will send?

Closed system - thermodynamics system, Closed System: The system tha...

Closed System: The system that can exchange energy with the surrounding but not the mass. The quantity of matter hence remains fixed. And the system can be described as cont

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