The electric field of a plane electromagnetic wave in vacuum is given by E = 30 (6 10¹⁰ t - 200 x ) j V/m . What is the amplitude of the magnetic field, and to which part of the electromagnetic spectrum does this wave belong?

Step-by-step solution

Given, E = 30 (6 10¹⁰ t - 200 x ) j V/m Comparing with the standard equation E = E₀ ( t - k x) j , we get: E₀ = 30 V/m = 6 10¹⁰ rad/s The amplitude of the magnetic field is: B₀ = E₀ c = 30 3 10^8 = 10⁻⁷ T The frequency of the electromagnetic wave is: f = 2 = 6 10¹⁰ 2 = 3 10¹⁰ Hz A frequency of 3 10¹⁰ Hz falls in the range of Microwaves (which typically span from 10^9 Hz to 3 10¹¹ Hz ). Answer: 10⁻⁷ T , Microwaves