Due to the presence of an em-wave whose electric component is given by $E = 100\sin(\omega t - kx)\ \text{N C}^{-1}$, a cylinder of length $200\ \text{cm}$ holds a certain amount of em-energy inside it. If another cylinder of the same length but half the diameter of the previous one holds the same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as
Answer: (B) $200\sin(\omega t - kx)\ \text{N C}^{-1}$
Energy stored $= u\times\text{volume}$, with average energy density $u \propto E_0^2$.
Halving the diameter makes the volume $\tfrac{1}{4}$ as large. For the same energy the energy density must be 4 times larger, so $E_0^2$ becomes $4\times$ and $E_0$ doubles:
$$E = 200\sin(\omega t - kx)\ \text{N C}^{-1}$$
Solution by Sreeraj P, M.Sc Physics