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

Steam turbines, The steam that leaves the super-heater is expanded from 130...

The steam that leaves the super-heater is expanded from 130bar at 535°C to 25.2bar at 310°C in a high pressure turbine. The steam from the exit of the HP turbine is reheated to 535

Phycics, digram of michelson inteferometer

digram of michelson inteferometer

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

Som, Strain energy stored in a body due to impact load

Strain energy stored in a body due to impact load

Noise attenuation in ventilating, Indicate size, capacity and noise reducin...

Indicate size, capacity and noise reducing characteristics of all silencers on plans, including silencers for vane-axial fans. Indicate all acoustical lining on drawings, genera

Design of a filament winding machine, How can I achieve a back and forth mo...

How can I achieve a back and forth movement of carriage system. How can I reverse the motor to go back and forth.

Pressure vessel materials, Pressure Vessel materials shall be as specified ...

Pressure Vessel materials shall be as specified on the Vessel Data Sheet. All attachments to vessels shall be of the same ‘P Number' material as that for the pressure envelope,

High resistance or low current in primary coil circuit, If High Resistance ...

If High Resistance or Low Current in Primary Coil Circuit Causes of Problem Remedy   Disconnected or loose wires

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