The electric field of a plane electromagnetic wave oscillates sinusoidally with a frequency of 2.0 × 10¹⁰ Hz and an amplitude of 60 Vm^-1. The wavelength (in cm) of the wave is (c = 3 × 10⁸ ms^-1): 

Given:

Frequency, \(\nu=2\times10^{10}Hz\)

Speed of light \(c=3\times10^8 m/s\)

Electric field Amplitude \(E_o=60Vm^{-1}\)

Concept:

When you consider an electromagnetic wave, the value of magnetic and electric fields keeps changing because of the wave at a point. If the wave is not a short pulse, the value of electric and magnetic fields keep changing at any point. For example, two points on a wave that attain their maximum value oscillate simultaneously.

Wavelength is defined as the distance between two most near points in phase with each other. Hence, two adjacent peaks or troughs on a wave are separated by a distance of a single complete wavelength.

The wave speed is equal to the product of its frequency and wavelength, and this implies the relationship between frequency and wavelength.

The wavelength of wave can be given by:

• \(\lambda=\frac{c}{\nu}\)

Explanation:

Put all values in above formula, we get,

\(\lambda=\frac{3\times10^8}{2\times10^{10}}m\)

\(\lambda=1.5\times10^{-2}m\)

\(\lambda=1.5cm\)

Hence, the correct answer is Option-\(\lambda=1.5cm\).