A plane electromagnetic wave with a magnetic field amplitude of 2 10⁻⁷ T falls normally on a non-reflecting surface of area 2 m ^2 . The total energy delivered to the surface in 1 minute is: (Take c = 3 10^8 m s ⁻¹ and ₀ = 4 10⁻⁷ T m A ⁻¹ )

Step-by-step solution

The intensity I of an electromagnetic wave in terms of its magnetic field amplitude B₀ is given by: I = B₀^2 c 2 ₀ Substitute the given values: I = (2 10⁻⁷)^2 (3 10^8) 2 (4 10⁻⁷) I = 4 10⁻¹⁴ 3 10^8 8 10⁻⁷ I = 12 10⁻⁶ 8 10⁻⁷ = 120 8 = 15 W m ⁻² The total energy E delivered to the surface is: E = I A t Given the area A = 2 m ^2 and time t = 1 minute = 60 s : E = ( 15 ) (2 ) 60 E = 30 60 = 1800 J Answer: 1800 J