The peak electric field in an intense IR laser beam is about 25,000 V/m. How much energy does this laser beam deliver in 1 minute if it makes a spot with a diameter of 2mm?

156.3 J

Explanation:

E = Amplitude of the electric field = 25000 V/m

t = time interval = 1 minute = 60 sec

d = diameter of the spot = 2 mm = 2 x 10⁻³ m

Area of the spot is given as

A = (0.25) πd²

A = (0.25) (3.14) (2 x 10⁻³) ²

A = 3.14 x 10⁻⁶ m²

Energy delivered to the spot is given as

U = (0.5) ε₀ E² c A t

Inserting the values

U = (0.5) (8.85 x 10⁻¹²) (25000) ² (3 x 10⁸) (3.14 x 10⁻⁶) (60)

U = 156.3 J