The equivalence of mass and energy expressed by the relation E = mc² is a fairly direct consequence of Maxwell’s conception of electromagnetic waves. According to Maxwell’s equations, the energy density of electric and magnetic fields e and b is (e² + b²)/(8p) and the momentum density is (e x b)/(4pc). Thus in the case of radiation (when e and b are equal and orthogonal) the energy density is E = e²/(4p) and the momentum density is p = e²/(4pc), so we have the important relation p = E/c. In addition, the energy of a pulse of light for relatively moving systems of reference transforms in proportion to its frequency, consistent with Planck’s relation E = hn. Given these facts, we can show that light pulses of total energy E reflecting inside a closed container contribute E/c² to the inertial mass (i.e., the resistance to acceleration) of the container.

this one I got from a site.

Here it states that, electric field=magnetic field(for light)

But in the ncert physics of class 12 and many other sites it is given that

E/c=B

E=electric field

B=Magnetic field

c=speed of light

So, which is correct

To clarify the relationship between electric and magnetic fields in the context of electromagnetic waves, let's break down the concepts and equations involved. The confusion often arises from the different ways these relationships are presented in various sources. Both statements you mentioned are correct, but they emphasize different aspects of electromagnetic theory.

Understanding Electromagnetic Waves

Maxwell's equations describe how electric fields (E) and magnetic fields (B) interact and propagate through space as electromagnetic waves. In a vacuum, these fields are indeed related, and for light waves, they have a specific relationship:

• The electric field (E) and magnetic field (B) are perpendicular to each other and to the direction of wave propagation.
• The magnitudes of these fields are related by the speed of light (c): E = cB.

Energy and Momentum in Electromagnetic Waves

When discussing energy density and momentum density in electromagnetic waves, we can refer to the equations derived from Maxwell's equations:

• The energy density (u) of the electric and magnetic fields is given by: u = (E² + B²) / (8π).
• The momentum density (p) is expressed as: p = (E x B) / (4πc).

For electromagnetic radiation, such as light, the electric and magnetic fields are equal in magnitude and orthogonal to each other. This leads to the simplification where we can express the energy density as:

u = E² / (4π) (since E = cB and B = E/c).

Relating Energy and Mass

Now, regarding the equivalence of mass and energy, Einstein's famous equation E = mc² indicates that energy (E) has mass equivalence. When light pulses reflect inside a closed container, they contribute to the inertial mass of that container. The energy of the light contributes an effective mass given by:

m = E/c².

This means that the energy of the light inside the container adds to the total mass of the system, affecting its resistance to acceleration.

Frequency and Energy Transformation

Additionally, when considering different reference frames, the energy of light pulses transforms according to their frequency, consistent with Planck's relation:

E = hν, where h is Planck's constant and ν is the frequency of the light.

Conclusion

In summary, both statements you encountered are correct but focus on different aspects of electromagnetic theory. The relationship E/c = B highlights the proportionality between electric and magnetic fields in electromagnetic waves, while the other emphasizes the energy-mass equivalence and how light contributes to the inertial mass of a system. Understanding these relationships is crucial for grasping the fundamental principles of physics, especially in the context of relativity and electromagnetism.