Electromagnetic Waves · Question 25

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

1. 50 ( t - kx) NC-1
2. 400 ( t - kx) NC-1
3. 200 ( t - kx) NC-1
4. 25 ( t - kx) NC-1

Answer

(3) 200 ( t - kx) NC-1

Solution

Average energy density: u = 12 0 E02

Energy in the cylinder: U = u d24l E02 d2 (same length l)

Same energy E0 d = constant

E0' = E0 dd' = 100 2 = 200 NC-1

E = 200 ( t - kx) NC-1

Answer: (3)