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Question:

A red LED emits light at 0.1 W uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is:

2.45 V/m

1.73 V/m

5.48 V/m

7.75 V/m

Solution:

Intensity: I = P/(4πr²)

where P is the power (0.1 W) and r is the distance (1 m).

I = 0.1 W / (4π(1 m)²)
I ≈ 0.00796 W/m²

The intensity (I) is also related to the amplitude of the electric field (E) by:

I = (1/2)ε₀cE²

where ε₀ is the permittivity of free space (8.854 x 10⁻¹² F/m) and c is the speed of light (3 x 10⁸ m/s).

Solving for E:

E = √(2I/(ε₀c))
E = √(2 * 0.00796 W/m² / (8.854 x 10⁻¹² F/m * 3 x 10⁸ m/s))
E ≈ 2.45 V/m