An LC circuit is used as a transmitter to generate electromagnetic waves in free space. If the circuit contains an inductor of inductance L = 2.5 ^2 mH and a capacitor of capacitance C = 1 F, what is the wavelength of the emitted electromagnetic wave? (Take the speed of light in vacuum c = 3 10^8 m/s)

Step-by-step solution

The frequency of the emitted electromagnetic wave is equal to the resonant frequency of the oscillating charge in the LC circuit. The resonant frequency is given by: f = 1 2 LC Given L = 2.5 ^2 10⁻³ H and C = 10⁻⁶ F, we have: LC = 2.5 10⁻⁹ ^2 = 25 10⁻¹⁰ ^2 LC = 5 10⁻⁵ s Substituting this into the frequency formula: f = 1 2 ( 5 10⁻⁵ ) = 1 10 10⁻⁵ = 10^4 Hz The wavelength of the electromagnetic wave in free space is: = c f = 3 10^8 10^4 = 3 10^4 m Answer: 3 10^4 m