The electric field associated with an electro magnetic wave in vacuum is given by E=i 40 (k z-6 × 10^8 t) , where E , z and t are in volt/m, metre and second respectively. The value of wave vector k is

Correct answer: A. 2 ~m^ -1 Electromagnetic wave equation E=E_0 (k w-ω t) Speed of electromagnetic wave v=(ω)/(k) Given, equation E= 40 (k z-6 × 10^8 t) i Comparing Eqs. (i) and (ii), we get ω=6 × 10^8 and E_0=40 i Here, wave factor k=(ω)/(v)=(6 × 10^8)/(3 × 10^8)=2 ~m^ -1

NEET 2012

Exam: NEET
Year: 2012
Subject: Physics
Chapter: Electromagnetic Waves

NEET 2012 · Physics · Electromagnetic Waves

The electric field associated with an electro magnetic wave in...

The electric field associated with an electro magnetic wave in vacuum is given by

\mathbf{E}=\mathbf{i}

40 \cos \left(k z-6 \times 10^8 t\right)

, where

E

z

and

t

are in volt/m, metre and second respectively. The value of wave vector

k

Options

A $2 \mathrm{~m}^{-1}$
B $0.5 \mathrm{~m}^{-1}$
C $6 \mathrm{~m}^{-1}$
D $3 \mathrm{~m}^{-1}$

Correct answer

A. $2 \mathrm{~m}^{-1}$

Step-by-step solution

Electromagnetic wave equation

E=E_0 \cos (k w-\omega t)

Speed of electromagnetic wave

v=\frac{\omega}{k}

Given, equation

\mathbf{E}= 40 \cos \left(k z-6 \times 10^8 t\right) \mathbf{i}

Comparing Eqs. (i) and (ii), we get

\omega=6 \times 10^8

and

E_0=40 \mathbf{i}

Here, wave factor

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

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