JEE MainPhysicsElectromagnetic Waves
The electric field of a plane electromagnetic wave propagating in free space is given by E = E₀ (kz - t) . The instantaneous magnetic energy density U_B associated with this wave is ( c is the speed of light in free space, ₀ is the permeability of free space):
Options
- AE₀^2 2 ₀ ^2(kz - t)
- BE₀^2 4 ₀ c^2 ^2(kz - t)
- C₀ E₀^2 2 c^2 ^2(kz - t)
- DE₀^2 2 ₀ c^2 ^2(kz - t)
Correct answer
D. E₀^2 2 ₀ c^2 ^2(kz - t)
Step-by-step solution
The instantaneous magnetic energy density is given by U_B = B^2 2 ₀ . For an electromagnetic wave, the magnitudes of the electric and magnetic fields are related by B = E c . Substituting this into the energy density formula gives: U_B = 1 2 ₀ ( E c )^2 = E^2 2 ₀ c^2 Given E = E₀ (kz - t) , we substitute this to find the instantaneous magnetic energy density: U_B = E₀^2 2 ₀ c^2 ^2(kz - t) Answer: E₀^2 2 ₀ c^2 ^2(kz - t)