The electric field of an electromagnetic wave in free space is given by E =10 (10^7 t+k x) j V / m , where t and x are in seconds and metres respectively. It can be inferred that (1) The wavelength λ is 188.4 ~m . (2)

Correct answer: D. (1) and (3) The electric field of electromagnetic wave aligned & E =10 (10^7 t ± kx) j & Amplitude =10 ~V/ m & c= ω k & 3 ×10^8= 10^7 k & or =(1)/(30) & or (2 π)/(λ)=(1)/(30) & or λ=188.4 ~m & aligned So, (1) and (3) option are correct.

NEET 2010

Exam: NEET
Year: 2010
Subject: Physics
Chapter: Electromagnetic Waves

NEET 2010 · Physics · Electromagnetic Waves

The electric field of an electromagnetic wave in free space is...

The electric field of an electromagnetic wave in free space is given by

\vec{E}=10 \cos \left(10^7 t+k x\right) \hat{j} V / m

, where

t

and

x

are in seconds and metres respectively. It can be inferred that (1) The wavelength

\lambda

188.4 \mathrm{~m}

. (2) The wave number

k

0.33 \mathrm{rad} / \mathrm{m}

. (3) The wave amplitude is

10 \mathrm{~V} / \mathrm{m}

. (4) The wave is propagating along.t

x

direction Which one of the following pairs of statements is correct?

Options

A(3) and (4)
B(1) and (2)
C(2) and (3)
D(1) and (3)

Correct answer

D. (1) and (3)

Step-by-step solution

The electric field of electromagnetic wave

\begin{aligned}& \overrightarrow{\mathrm{E}}=10 \cos \left(10^7 \mathrm{t} \pm \mathrm{kx}\right) \hat{\mathrm{j}}\\ & \text{ Amplitude }=10 \mathrm{~V}/ \mathrm{m}\\ & \because \quad \mathrm{c}=\frac{\omega}{\mathrm{k}}\\ & \therefore \quad 3 \times10^8=\frac{10^7}{\mathrm{k}}\\ & \text{ or } \quadk=\frac{1}{30}\\ & \text{ or } \quad \frac{2 \pi}{\lambda}=\frac{1}{30}\\ & \text{ or } \quad \lambda=188.4 \mathrm{~m}\\ & \end{aligned}

So, (1) and (3) option are correct.

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