The electric field of an electromagnetic wave in free space is given by E = 10cos (10⁷t + kx)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) the wave number k is 0.33 rad/m. (3) the wave amplitude is 10 V/m. (4) the wave is propagating along +x direction. Which one of the following pairs of statements is correct? (a) (3) and (4) (b) (1) and (2) (c) (2) and (3) (d) (1) and (3)

Answer: (d). ω = 10⁷ rad/s, k = ω/c = 10⁷3×10⁸ = 0.033 rad/m, so (2) is false. λ = 2π/k = 2π×30 = 188.4 m, so (1) is true. Amplitude = 10 V/m, so (3) is true; (ω t + kx) means travel along -x, so (4) is false. So the answer is (d) (1) and (3).

The electric field of an electromagnetic wave in free space is given… | NEET 2010 (AIPMT, Mains)

Q87NEET 2010 · AIPMT · MAINSMedium

Nature of EM Waves & Wave Equation

The electric field of an electromagnetic wave in free space is given by $\vec{E} = 10\cos(10^{7}t + kx)\hat{j}\text{ V/m},$ where t and x are in seconds and metres respectively. It can be inferred that

(1) the wavelength $\lambda$ is 188.4 m.

(2) the wave number k is 0.33 rad/m.

(3) the wave amplitude is 10 V/m.

(4) the wave is propagating along +x direction.

Which one of the following pairs of statements is correct?

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Answer: (d)

$\omega = 10^{7}$ rad/s, $k = \omega/c = \dfrac{10^{7}}{3\times10^{8}} = 0.033$ rad/m, so (2) is false.
$\lambda = 2\pi/k = 2\pi\times30 = 188.4$ m, so (1) is true.
Amplitude $= 10$ V/m, so (3) is true; $(\omega t + kx)$ means travel along $-x$ , so (4) is false.
So the answer is (d) (1) and (3).

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