An electromagnetic wave has an electric field given by $\vec { E } = - \left( 9.0 \times 10 ^ { 5 } \mathrm {~V} / \mathrm { m } \right) \hat { j } \cos \left[ \left( 9.42 \times 10 ^ { 15 } \mathrm { rad } / \mathrm { s } \right) t - k z \right]$ . The wavelength of the wave is
A) $2.0 \times 10 ^ { - 7 } \mathrm {~m}$
B) $2.0 \times 10 ^ { 7 } \mathrm {~m}$
C) $9.99 \times 10 ^ { 6 } \mathrm {~m}$
D) $3.1 \times 10 ^ { 7 } \mathrm {~m}$

Question

Quizplus · Accepted Answer

The wavelength $\lambda$ of an electromagnetic wave is related to its wave number $k$ and the speed of light $c$ by the equation $\lambda = \frac{2\pi}{k}$. Given the electric field equation, we can identify the angular frequency $\omega = 9.42 \times 10^{15} \, \text{rad/s}$ and use the relation $\omega = 2\pi f = \frac{2\pi c}{\lambda}$ to find the wavelength. Since the speed of light $c = 3.00 \times 10^8 \, \text{m/s}$, we can solve for $\lambda$. Rearranging the equation gives $\lambda = \frac{2\pi c}{\omega}$. Substituting the given values, $\lambda = \frac{2\pi \times 3.00 \times 10^8}{9.42 \times 10^{15}}$, which calculates to approximately $2.0 \times 10^{-7} \, \text{m}$.

An Electromagnetic Wave Has an Electric Field Given By the Wavelength of the Wave Is A)

An Electromagnetic Wave Has an Electric Field Given By the Wavelength of the Wave Is
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