Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Waves
Determine the amplitudes of the electric and magnetic fields in a laser beam that has an intensity of 2.5 10¹⁴ W m ⁻² .
Options
- A4.3 10⁸ N C ⁻¹ , 1.44 T
- B2.1 10⁸ N C ⁻¹ , 0.72 T
- C6.1 10⁸ N C ⁻¹ , 2.04 T
- D3.1 10⁸ N C ⁻¹ , 1.02 T
Correct answer
A. 4.3 10⁸ N C ⁻¹ , 1.44 T
Step-by-step solution
The intensity of an electromagnetic wave is given by the relation: I = 1 2 ₀ c E₀^2 where E₀ is the amplitude of the electric field, ₀ is the permittivity of free space, and c is the speed of light in vacuum. Rearranging for E₀ : E₀ = 2I ₀ c Substituting the given values I = 2.5 10¹⁴ W m ⁻² , ₀ = 8.85 10⁻¹² C ^2 N ⁻¹ m ⁻² , and c = 3 10^8 m s ⁻¹ : E₀ = 2 2.5 10¹⁴ 8.85 10⁻¹² 3 10^8 E₀ = 5 10¹⁴ 26.55 10⁻⁴ E₀ = 18.83 10¹⁶ 4.34 10^8 N C ⁻¹ The amplitude of the magnetic field B₀ is related to E₀ by: B₀ = E₀ c Substituti