Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Waves
In a plane electromagnetic wave, the magnetic field is expressed as B = (200 T ) ! [(4.0 10¹⁵ s ⁻¹)(t - x/c) ] . Determine the maximum electric field and the average energy density associated with the electric field.
Options
- A6 10⁴ N C ⁻¹ , 0.016 J m ⁻³
- B3 10⁴ N C ⁻¹ , 0.008 J m ⁻³
- C1.2 10⁵ N C ⁻¹ , 0.032 J m ⁻³
- D6 10⁴ N C ⁻¹ , 0.008 J m ⁻³
Correct answer
D. 6 10⁴ N C ⁻¹ , 0.008 J m ⁻³
Step-by-step solution
Given B₀ = 200 T = 2 10⁻⁴ T . The maximum electric field is given by: E₀ = c B₀ = (3 10⁸ m s ⁻¹) (2 10⁻⁴ T ) = 6 10⁴ N C ⁻¹ The average energy density associated with the electric field is: u_ E = 1 4 ₀ E₀² Using ₀ = 1 36 10⁹ F m ⁻¹ , we get: u_ E = 1 4 1 36 10⁹ (6 10⁴)² u_ E = 1 4 1 36 10⁹ 36 10⁸ = 10⁻¹ 4 = 0.1 12.56 0.008 J m ⁻³