The total energy density for an electromagnetic wave in vacuum is:

• A. ε₀ E² / 3
• B. ε₀ E²
• C. ε₀ E² / 2
• D. E² / ε₀

The total energy density of an electromagnetic wave in a vacuum can be derived from the contributions of both the electric and magnetic fields. The energy density (u) is given by the formula:

Energy Density Formula

The total energy density is the sum of the electric energy density and the magnetic energy density:

• Electric energy density: u_E = (1/2) ε₀ E²
• Magnetic energy density: u_B = (1/2) (B²/μ₀)

Relationship Between Electric and Magnetic Fields

In a vacuum, the electric field (E) and magnetic field (B) are related by the equation:

B = E/c, where c is the speed of light.

Total Energy Density Calculation

By substituting B into the magnetic energy density formula, we can express the total energy density:

u = u_E + u_B = (1/2) ε₀ E² + (1/2) (E²/μ₀c²)

Since μ₀c² = 1/ε₀, this simplifies to:

u = (1/2) ε₀ E² + (1/2) ε₀ E² = ε₀ E²

Final Answer

The correct answer is B. ε₀ E².