Uniform alternate electric field, Mechanical Engineering

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

Posted Date: 9/18/2012 1:06:00 AM | Location : United States







Related Discussions:- Uniform alternate electric field, Assignment Help, Ask Question on Uniform alternate electric field, Get Answer, Expert's Help, Uniform alternate electric field Discussions

Write discussion on Uniform alternate electric field
Your posts are moderated
Related Questions
Explain the semi universal drilling machine The semi universal drilling machine this machines, in addition to the above three basic movements, carry provision for swinging of

Define the Boundary Representation of solids Boundary model or b-rep model is based on the topological notion that a physical object is bounded by a set of faces. These faces a


Remove cover left crank case and check for leakage: Before attending oil seal leakage check if any leak is there in the highlighted points - Neutral switch "o" ring leak, Shifter

Base Circle: this is the smallest circle tangent to the cam profile. Trace Point: this is theoretical point on the follower whose motion explained the movement of the foll

Pole core and pole shoe The pole cores are made of steel laminations that are insulated from each other and riveted together. Every pole core has a pole shoe having a curved su

Determine the analytical solution for the maximum stress in the member shown. Submit screen shots that show the shape of the elements that result with a global element size of 0.15

SIGNIFICANCE OF DEFECTS IN WELDS   In the correct sense of the word, a defect is a rejectable discontinuity or a flaw of rejectable nature. Certain flaws acceptable in one t

which aero-gas turbine engine is used in T5 aircraft

Explain the Construction of dc machine The constructional features of a dc machine are given below. A dc machine has two major parts, magnetic ?eld system and armature. The ?eld