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 = E_{0} sin ω t = ( E_{0} i) sin ω t (i)where, E_{0} 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 c_{1} is set by initial condition: at t = 0, when E = 0, let v = v_{0}. Hence, we get Integrating once again, we find where constant of integration r_{0} is the initial position of the particle; at t = 0, r = r_{0}.We can always put r_{0} = 0; let us also take v_{0} = 0. Further, if E_{0} = E_{0} i, we have The particle moves along X-axis with time dependent speed v_{x} (t). The average speed of the particle during a cycle is, v_{x} 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 = x_{1} + x_{2} If v_{0} ≠ 0, the particle may continue to move along y and z directions with constant initial velocities v_{oy} and v_{oz}. Simultaneously, it is drifted towards X-axis by a fixed distance per cycle, viz.