Energy Density

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For a plane electromagnetic wave propagating in vacuum, how does the average energy stored in the electric field compare with that stored in the magnetic field?

RankGuru · Accepted Answer

According to NCERT Class 12, Chapter 8 (Electromagnetic Waves), the energy carried by an electromagnetic wave is shared between its electric and magnetic components at every point in space. The electric energy density is u_E = ½ε₀E², and the magnetic energy density is u_B = B²/(2μ₀); these are the same expressions met earlier in electrostatics and magnetism, now applied to the fields of a travelling wave. Using the relation E = cB together with c = 1/√(μ₀ε₀), one can show that u_E = u_B at every instant. Hence the energy is equally divided between the two fields, and the total energy density is simply twice either part. Because both fields oscillate in phase, this equality holds not only on average but at each moment of the cycle. The option claiming the electric field stores twice the magnetic energy is wrong because substitution of E = cB shows exact equality, not a factor of two. Similarly, the claim that the magnetic field stores twice the electric energy contradicts the same derivation. The statement that the electric field stores all the energy ignores the genuine magnetic contribution. A consistency check using E = cB confirms u_E = ½ε₀c²B² = B²/(2μ₀) = u_B, so equal sharing is the correct conclusion.

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