Question

The ratio of average electric energy density and total average energy density of an electromagnetic wave is:

• A. 2
• B. \( \frac{1}{2} \)
• C. 1
• D. 3

Hint:

In an electromagnetic wave, the electric and magnetic energy densities are equal, and the total energy density is twice the electric energy density.

Answer 1

The Correct Option is B

Step 1: Formula for energy densities in an electromagnetic wave. The total energy density \( u_{{total}} \) in an electromagnetic wave is the sum of the electric and magnetic energy densities. The electric energy density \( u_E \) and magnetic energy density \( u_B \) are given by: \[ u_E = \frac{\epsilon_0 E^2}{2}, \quad u_B = \frac{B^2}{2 \mu_0} \] where \( \epsilon_0 \) is the permittivity of free space, \( \mu_0 \) is the permeability of free space, \( E \) is the electric field, and \( B \) is the magnetic field. 
Step 2: Relationship between electric and magnetic fields. In an electromagnetic wave, the energy density is equally distributed between the electric and magnetic fields, so: \[ u_E = u_B \] 
Step 3: Total energy density. The total energy density is the sum of the electric and magnetic energy densities: \[ u_{{total}} = u_E + u_B = 2u_E \] Step 4: Ratio of average electric energy density to total energy density. The ratio is: \[ \frac{u_E}{u_{{total}}} = \frac{u_E}{2u_E} = \frac{1}{2} \] Thus, the ratio of average electric energy density to total average energy density is \( \frac{1}{2} \).