Due to presence of an em-wave whose electric component is given by E = 100 sin ( ω t − kx ) NC − 1 , a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of sam

Question

Due to presence of an em-wave whose electric component is given by E = 100 sin ( ω 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

TestHub · Accepted Answer

Energy density of an E M wave ​ = 2 1 ​ ε E 0 2 ​ , whare E 0 ​ is the amplitude of the wave. Since total energy is same for both cylinders ​ ( 2 1 ​ ε E 1 2 ​ ) π R 1 2 ​ L 1 ​ = ( 2 1 ​ ε E 2 2 ​ ) π R 2 2 ​ L 2 ​ ⇒ E 1 2 ​ R 1 2 ​ L 1 ​ = E 2 2 ​ R 2 2 ​ L 2 ​ or E 2 ​ = R 2 ​ E 1 ​ R 1 ​ ​ L 2 ​ L 1 ​ ​ ​ = ( d /2 ) 100 d ​ L 1 L 1 ​ ​ ​ = 200 N / C [ ∵ L 1 ​ = L 2 ​ = 200 cm ] ​ ⇒ The amplitude of corresponding EM wave is 200 N/C or the wave is E = 200 sin ( ω t − k x ) NC − 1

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