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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, Integrating, we find where constant of integration c1 is set by initial condition: at t = 0, when E = 0, let v = v0. Hence, we get Integrating once again, we find where constant of integration r0 is the initial position of the particle; at t = 0, r = r0.We can always put r0 = 0; let us also take v0 = 0. Further, if E0 = E0 i, we have The particle moves along X-axis with time dependent speed vx (t). The average speed of the particle during a cycle is, vx is called the drift velocity of the particle. The displacement of the particle during one complete cycle, i.e. in time T, The graph between x and t is obtained by superposing the sine curve and the straight line,x = x1 + x2 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.
Heat distribution in spot welding Besides the resistance at the interface, there are six other resistance through which the same welding current is passed. They are: Res
Transverse Electric Field Consider a charged particle (e.g. an electron) moving along X-axis with constant velocity v , i . At x = 0 , it enters into a region where a unif
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Determine the number of cycles - crack propagation: The plate of above Example contained a crack of 50 mm length in the centre before it was subjected to cyclic stress. Deter
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