Question

In an electromagnetic wave, the ratio of energy densities of electric and magnetic fields is ______.
Fill in the blank with the correct answer from the options given below

• A. 1 : 1
• B. 1 : c
• C. c : 1
• D. \(1 : c^2\)

Answer 1

The Correct Option is A

Let's analyze the energy densities of electric and magnetic fields in an electromagnetic wave.

Energy Density of Electric Field (u_E):

u_E = (1/2)ε₀E²

Where:

• ε₀ is the permittivity of free space
• E is the electric field strength

Energy Density of Magnetic Field (u_B):

u_B = (1/2)(B²/μ₀)

Where:

• μ₀ is the permeability of free space
• B is the magnetic field strength

Relationship between E and B in an Electromagnetic Wave:

In an electromagnetic wave, the electric field (E) and magnetic field (B) are related by:

E = cB

Where c is the speed of light.

Ratio of Energy Densities:

We want to find the ratio u_E/u_B:

u_E/u_B = [(1/2)ε₀E²] / [(1/2)(B²/μ₀)]

u_E/u_B = ε₀E²μ₀/B²

Substituting E = cB:

u_E/u_B = ε₀(cB)²μ₀/B²

u_E/u_B = ε₀c²μ₀

We know that c = 1/√(ε₀μ₀), so c² = 1/(ε₀μ₀).

Therefore, ε₀μ₀ = 1/c².

Substituting this into the ratio:

u_E/u_B = ε₀μ₀c² = (1/c²)c² = 1

Thus, u_E/u_B = 1, which means u_E : u_B = 1 : 1.

The correct answer is:

Option 1: 1 : 1