The statement that the energy in the magnetic field is equal to that in the electric field is a fundamental property of electromagnetic waves. However, it is true that in an electromagnetic wave, the magnetic field strength is weaker compared to the electric field strength. This can be explained intuitively without delving into mathematical details.
An electromagnetic wave consists of oscillating electric and magnetic fields that are perpendicular to each other and propagate through space. When an electromagnetic wave is generated, the electric field is initially dominant and reaches its maximum strength. As the wave propagates, the electric field starts to diminish, while the magnetic field grows in strength. At the midpoint of the wave's cycle, the electric field becomes zero, and the magnetic field reaches its maximum strength. The process then repeats as the wave continues to propagate.
The reason for the apparent difference in strength between the electric and magnetic fields lies in the way electromagnetic waves are generated. In most cases, electromagnetic waves are created by accelerating electric charges, such as in an antenna or by the motion of electrons in an atom. Due to the properties of these charge distributions, the electric field tends to be stronger near the source, while the magnetic field lags behind.
Another way to think about it is in terms of the behavior of charged particles. Electric fields can exert forces on charged particles, causing them to accelerate and move. However, magnetic fields can only exert forces on moving charged particles. Since most objects around us are not constantly in motion, the effect of magnetic fields is typically weaker in comparison.
Therefore, while the energy in the magnetic field is indeed equal to that in the electric field, the apparent weakness of the magnetic field in an electromagnetic wave can be attributed to the nature of its generation and the different ways in which electric and magnetic fields interact with charged particles.