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  • The electric field associated with an electro magnetic wave in vacuum, is given by <img alt="\mathrm{\mathrm{E}=\mathrm{i}40 \cos \left(k z-6 \times 10^8 \mathrm{t}\right)}" src="https://entranceco

The electric field associated with an electro magnetic wave in vacuum, is given by \mathrm{\mathrm{E}=\mathrm{i}40 \cos \left(k z-6 \times 10^8 \mathrm{t}\right)}, where E,z and t are in Volt/m, metre and second, respectively. The value of wave vector k is

Option: 1

2\; \text{m}^{-1}


Option: 2

0.5\; \text{m}^{-1}


Option: 3

6\; \text{m}^{-1}


Option: 4

3\; \text{m}^{-1}


Answers (1)

best_answer

Electromagnetic wave equation,

                        \mathrm{E=E_0 \cos (k z-\omega t)\: \: \: \: \: \: \: \: \: \: \: \: ......(i)}

Spped of electromagnetic wave, \mathrm{v=\frac{\omega}{k}}

Given, equation 

                        \mathrm{E=140 \cos \left(k z-6 \times 10^8 t\right)\: \: \: \: \: \: \: \: ...(ii)}

On comparing Eqs. (i) and (ii), we get

                                \mathrm{\omega=6 \times 10^8}

  and                         \mathrm{E_0=40 i}

Here, wave factor \mathrm{k=\frac{\omega}{v}=\frac{6 \times 10^8}{3 \times 10^8}=2 \mathrm{~m}^{-1}} 

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