Short Answer

The average energy stored in electromagnetic (EM) waves is the total energy carried by the electric and magnetic fields, averaged over one complete cycle of the wave. Since both fields store energy, the average energy is shared equally between them. This means half of the total energy is in the electric field and the other half is in the magnetic field.

The average energy depends on the amplitude of the fields. Higher amplitude means more stored energy. The average energy tells us how much energy the wave transports through space over time, which is useful for studying intensity, power flow, and radiation effects.

Detailed Explanation :

Average Energy Stored in EM Waves

Electromagnetic waves carry energy as they move through space or through a medium. This energy is stored in two components of the wave: the electric field and the magnetic field. Both fields oscillate together and continuously exchange energy. Because of this oscillation, the energy stored at any instant keeps changing between maximum and minimum values. To properly describe the energy carried by EM waves, physicists use the concept of average energy, which represents the average amount of energy stored over a complete cycle of the wave.

The average energy stored in EM waves gives a realistic and stable value for understanding how much energy is transported per unit volume. Since the fields vary sinusoidally (like a smooth wave), their instantaneous energy also varies sinusoidally. The average energy helps eliminate these fluctuations and gives a steady value for practical use.

1. Electric Field Contribution to Average Energy

The electric field stores energy whenever it is present. But in an EM wave, the electric field oscillates, so it constantly changes in magnitude. At some points, it reaches maximum value; at others, it becomes zero.

Because of this variation, the energy stored also fluctuates. To find average energy, we take the average of this changing electric energy over one full wave cycle.

The average electric energy density is proportional to the square of the electric field amplitude. This means:

• Higher electric field amplitude → higher average energy
• Lower electric field amplitude → lower average energy

Even though the instantaneous electric energy changes continuously, the average value remains constant.

2. Magnetic Field Contribution to Average Energy

Similar to the electric field, the magnetic field also changes throughout the wave. As it oscillates, the magnetic energy increases and decreases. The pattern of energy variation is the same as that of the electric field because the two fields are linked and remain in phase.

The average magnetic energy also depends on the square of the magnetic field amplitude. Just like the electric field, the magnetic field contributes half of the total average energy.

Thus:

• Electric field average energy = half of total energy
• Magnetic field average energy = other half of total energy

This equal sharing is one of the most important properties of EM waves.

3. Total Average Energy of EM Waves

The total average energy stored in an EM wave is the sum of:

• Average electric energy
• Average magnetic energy

Because both components contribute equally, the total average energy can be expressed simply as twice the average of either field’s energy.

This shows a perfect balance in EM waves, where neither field dominates. The wave consists of a harmonious combination of electric and magnetic energy.

4. Dependence on Amplitude

The average energy stored in EM waves increases when the amplitude of either the electric or magnetic field increases. This relationship is not linear; it is quadratic. Meaning:

• If amplitude doubles, the energy becomes four times
• If amplitude triples, the energy becomes nine times

This strong dependence means even small changes in amplitude cause large changes in energy. For this reason, amplitude is considered a very important factor in controlling how much energy an EM wave carries.

5. Relation to Intensity and Power

Intensity of an EM wave is defined as the power delivered per unit area. Intensity directly depends on the average energy density. As average energy density increases, the intensity increases.

Thus, average energy stored in EM waves helps determine:

• Brightness of light
• Strength of radio signals
• Heating in microwaves
• Power of lasers
• Strength of radiation

This close relationship shows that average energy is a key factor in understanding how EM waves interact with matter.

6. Physical Meaning of Average Energy

The average energy gives a true measure of the wave’s ability to:

• Transport energy
• Perform work
• Heat objects
• Apply radiation pressure
• Generate power in communication systems

Because instantaneous energy constantly changes, using average energy provides a reliable and meaningful value for calculations and real-world applications.

7. Importance in Real Life

Average energy stored in EM waves is important in many technologies:

• Solar panels depend on average solar radiation energy.
• Microwave ovens rely on average microwave energy to heat food.
• Radio broadcasting uses average signal energy to determine coverage.
• Medical imaging uses average X-ray energy for safe diagnosis.
• Laser engineering uses average energy to cut or weld materials.

Scientists and engineers use average energy values to make accurate and safe designs.

Conclusion

The average energy stored in electromagnetic waves is the combined energy of the electric and magnetic fields averaged over a full cycle. Both fields share energy equally, and the total average energy depends strongly on amplitude. This average energy is crucial for understanding wave intensity, power, and real-world applications like communication, heating, lighting, and imaging. It provides a stable and meaningful measure of the energy carried by EM waves.