In an electromagnetic wave, the electric and magnetic fields oscillate perpendicular to each other and to the direction of wave propagation. As the wave propagates through space, the electric and magnetic fields continuously regenerate themselves through a process called self-induction.
When an electromagnetic wave reaches the point of zero field value (half the wavelength), it doesn't mean that the fields disappear entirely. Rather, the fields change their direction and start to increase in the opposite direction. This reversal occurs because electromagnetic waves are sinusoidal in nature, and they oscillate back and forth.
The changing magnetic field induces an electric field, and the changing electric field induces a magnetic field, through the process of electromagnetic induction. This mutual induction allows the fields to regenerate themselves as the wave progresses.
The electric and magnetic fields continually interact and sustain each other as the wave propagates. This interplay between the electric and magnetic fields creates a self-sustaining wave that carries energy and information through space.