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.