When a charge begins to move, it creates a disturbance in the fields. This disturbance propagates out from the charge at the speed of light. Although the speed of light is very great, it is finite. Note that in the last frame of the fieldline movie, the disturbance has not reached the point P. Therefore, the fields at that point are not evaluated using the particle's present position, but are evaluated assuming the particle is still at rest at its initial point, that is, the fields are actually seeing the particle at an earlier moment in time called the retarded time.
This is the reason when we view light coming from a distanct star we are not seeing the star in its present state but as it was at an earlier time. The greater the distance of the star from us, the greater is the time retardation. Let t be the present time, t' the retarded time, and r be the distance from a source at t'. The fields are to be evaluated according to t':
This introduces a complication. The field at P must not be evaluated according to the charges present position but according to where the charge was before the acceleration began! This retarded time problem increases the complexity of the calculations tremendously and is the reason we need a computer to do the calculations for us.
Go to Exercise 2.