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The electric field of a plane electromagnetic wave oscillates sinusoidally with a frequency of 2.0 × 101010^{10}1010​ Hz and an amplitude of 60 V
Question

The electric field of a plane electromagnetic wave oscillates sinusoidally with a frequency of 2.0 × 101010^{10}​ Hz and an amplitude of 60 Vm1\text{Vm}^{-1}​. The wavelength (in cm) of the wave is (c = 3 × 108 ms110^8\space\text{ms}^{-1}​):

A.

1.5

B.

0.015

C.

0.66

D.

0.15

Correct option is A

To calculate the wavelength of the electromagnetic wave, we use the formula:c=λfWhere:c=speed of light in a vacuum (3×108 m/s),λ=wavelength of the wave,f=frequency of the wave.Given:c=3×108 m/s,f=2.0×1010 Hz.We can rearrange the formula to solve for wavelength:λ=cfSubstitute the given values:λ=3×1082.0×1010=0.015 m=1.5 cm\text{To calculate the wavelength of the electromagnetic wave, we use the formula:} \\c = \lambda \cdot f \\\text{Where:} \\c = \text{speed of light in a vacuum} \, (3 \times 10^8 \, \text{m/s}), \\\lambda = \text{wavelength of the wave}, \\f = \text{frequency of the wave}. \\\text{Given:} \\c = 3 \times 10^8 \, \text{m/s}, \\f = 2.0 \times 10^{10} \, \text{Hz}. \\\text{We can rearrange the formula to solve for wavelength:} \\\lambda = \frac{c}{f} \\\text{Substitute the given values:} \\\lambda = \frac{3 \times 10^8}{2.0 \times 10^{10}} = 0.015 \, \text{m} = 1.5 \, \text{cm}​​

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