Due to presence of an em-wave whose electric component is given by E =100 ( t - kx ) NC ⁻¹ , a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Step-by-step solution

Energy density of an E M_ wave = 1 2 E₀^2 , whare E₀ is the amplitude of the wave. Since total energy is same for both cylinders aligned & ( 1 2 E₁^2 ) R₁^2 L₁= ( 1 2 E₂^2 ) R₂^2 L₂ & E₁^2 R₁^2 L₁=E₂^2 R₂^2 L₂ & or E₂= E₁ R₁ R₂ L₁ L₂ = 100 ~d ( ~d / 2) L₁ L 1 =200 ~N / C & [ L₁=L₂=200 ~cm ] aligned The amplitude of corresponding E M wave is 200 N/C or the wave is E=200 ( t-k x) NC ⁻¹