A plane electromagnetic wave with a magnetic field amplitude of 2 ×...

The intensity $I$ of an electromagnetic wave in terms of its magnetic field amplitude $B_0$ is given by:

$I = \dfrac{B_0^2 c}{2\mu_0}$

Substitute the given values:
$I = \dfrac{(2 \times 10^{-7})^2 \times (3 \times 10^8)}{2 \times (4\pi \times 10^{-7})}$

$I = \dfrac{4 \times 10^{-14} \times 3 \times 10^8}{8\pi \times 10^{-7}}$

$I = \dfrac{12 \times 10^{-6}}{8\pi \times 10^{-7}} = \dfrac{120}{8\pi} = \dfrac{15}{\pi} \text{ W m}^{-2}$

The total energy $E$ delivered to the surface is:
$E = I \times A \times t$

Given the area $A = 2\pi \text{ m}^2$ and time $t = 1 \text{ minute} = 60 \text{ s}$:
$E = \left(\dfrac{15}{\pi}\right) \times (2\pi) \times 60$

$E = 30 \times 60 = 1800 \text{ J}$

Answer: $1800 \text{ J}$