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29 December, 14:43

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?

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  1. 29 December, 15:22
    0
    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
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