Question

The property which is not of an electromagnetic wave travelling in free space is that :

• A. they are transverse in nature.
• B. the energy density in electric field is equal to energy density in magnetic field.
• C. they travel with a speed equal to \(\frac{1}{\sqrt{\mu_0\epsilon_0}}\).
• D. they originate from charges moving with uniform speed.

Answer 1

The Correct Option is D

Electromagnetic waves are a fundamental concept in physics, especially when discussing their propagation through free space. Here, we analyze the given options to identify the property not applicable to electromagnetic waves traveling in free space.

1. Electromagnetic waves are transverse in nature. This means that the electric and magnetic fields oscillate perpendicular to the direction of wave propagation.
2. The energy density in the electric field is indeed equal to the energy density in the magnetic field for these waves. The energy (U) is given as \(U = \frac{1}{2}(\epsilon_0E^2 + \frac{B^2}{\mu_0})\), where \(E\) is the electric field, \(B\) is the magnetic field, \(\epsilon_0\) is the permittivity of free space, and \(\mu_0\) is the permeability of free space.
3. They travel with a speed \(\frac{1}{\sqrt{\mu_0\epsilon_0}}\), known as the speed of light in free space, approximately \(3 \times 10^8\) m/s.
4. Electromagnetic waves do not originate from charges moving with uniform speed. Instead, they are produced by accelerated charges or time-varying currents. This property is the correct answer because charges moving with constant (uniform) speed do not produce changing electromagnetic fields.

Therefore, the statement that electromagnetic waves "originate from charges moving with uniform speed" is not true for those traveling in free space.

Answer 2

Step 1: Analyze the Properties of Electromagnetic Waves

Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation, making them transverse in nature.

Their energy density in the electric and magnetic fields is equal.

They travel in free space with a speed:

$$ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} $$

Where:

\( c \) = Speed of electromagnetic waves in free space

\( \mu_0 \) = Permeability of free space

\( \epsilon_0 \) = Permittivity of free space

Step 2: Address the Incorrect Property

Electromagnetic waves are produced by accelerated charges, not charges moving with uniform speed. Thus, option (3) is incorrect.

Step 3: Conclusion

The property not belonging to electromagnetic waves is that they originate from charges moving with uniform speed.