Question

An electric charge oscillating with a frequency of 1 kilo cycles/s can radiates electromagnetic waves of wavelength (A) \(100 \mathrm{~km}\) (B) \(200 \mathrm{~km}\) (C) \(300 \mathrm{~km}\) (D) \(400 \mathrm{~km}\)

Short answer

The wavelength of the radiated electromagnetic waves emitted by an electric charge oscillating with a frequency of 1 kilo cycles/s can be found using the formula \(c = f \cdot \lambda\), where 'c' is the speed of light, 'f' is the frequency, and '\(\lambda\)' is the wavelength. By substituting the given values, we find the wavelength to be \(300~km\). Thus, the correct answer is (C) 300 km.

Step-by-step solution

Write down the given information and formula

We are given the frequency (f) of the oscillating electric charge as 1 kilo cycles/s or 1000 cycles/s. So, \(f = 1000~Hz\) Also, we know that the speed of light (c) is approximately \(3 \cdot 10^8~m/s\). The formula that relates frequency, wavelength, and the speed of light is: \(c = f \cdot \lambda\) where 'c' is the speed of light, 'f' is the frequency, and '\(\lambda\)' is the wavelength.

Solve for wavelength

We know the frequency (f) and the speed of light (c), so we can find the wavelength by rearranging the formula: \(\lambda = \frac{c}{f}\) Now, plug in the values of 'c' and 'f': \(\lambda = \frac{3 \cdot 10^8~m/s}{1000~Hz}\)

Calculate the wavelength

Now, calculate the wavelength: \(\lambda = \frac{3 \cdot 10^8}{1000}\) \(\lambda = 3 \cdot 10^5~m\) Since 1 km = 1000 m, \(\lambda = \frac{3 \cdot 10^5~m}{1000} = 300~km\)

Compare with the options and choose the correct one

Comparing the calculated value of the wavelength with the given options, we can see that the correct answer is: (C) 300 km