show that electromagnetic wave is produced when charge is accelerated?

When a charge is accelerated, it creates changes in the electric and magnetic fields around it, leading to the production of electromagnetic waves. To understand this phenomenon, let's break it down step by step.

The Basics of Charge and Fields

First, it's essential to recognize that electric charges generate electric fields. When a charge is stationary, it creates a static electric field that radiates outward. However, when that charge begins to move or accelerate, the situation changes significantly.

Acceleration and Field Changes

Acceleration refers to any change in the velocity of a charge, which can include speeding up, slowing down, or changing direction. According to Maxwell's equations, which govern electromagnetism, an accelerating charge produces a changing electric field. This change in the electric field, in turn, induces a magnetic field.

Creating Electromagnetic Waves

As the charge continues to accelerate, these changing electric and magnetic fields propagate outward from the charge at the speed of light. This propagation forms what we call an electromagnetic wave. The key points to note are:

• Electric Field (E): The changing electric field is perpendicular to the direction of wave propagation.
• Magnetic Field (B): The induced magnetic field is also perpendicular to both the electric field and the direction of propagation.
• Wave Propagation: The combination of these fields creates a self-sustaining wave that travels through space.

Example of Electromagnetic Wave Production

A classic example of this phenomenon is a radio antenna. When an alternating current flows through the antenna, it causes the charges within the antenna to accelerate back and forth. This acceleration generates changing electric and magnetic fields, which then radiate away from the antenna as electromagnetic waves. These waves can carry information, such as radio signals, over vast distances.

Analogy for Better Understanding

Think of a stone thrown into a calm pond. The stone creates ripples that spread outwards. In this analogy, the stone represents the accelerating charge, and the ripples represent the electromagnetic waves. Just as the ripples are caused by the disturbance of the water, electromagnetic waves are generated by the disturbance in the electric and magnetic fields due to the acceleration of the charge.

Conclusion

In summary, when a charge is accelerated, it alters the surrounding electric and magnetic fields, leading to the generation of electromagnetic waves. This fundamental principle is crucial in understanding various technologies, from radio communications to the behavior of light itself. The interplay between electric and magnetic fields is a cornerstone of electromagnetism and illustrates the profound connection between electricity and magnetism.