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Question:

A lamp emits monochromatic green light uniformly in all directions.

4.02 V/m

1.34 V/m

5.36 V/m

2.68 V/m

Solution:

The provided data is incomplete. To solve a problem related to the intensity or electric field of light emitted from a lamp, we need additional information such as:

  • Power of the lamp (P): This is usually measured in Watts (W) and represents the rate at which the lamp emits energy as light.
  • Distance from the lamp (r): The intensity and electric field strength of the light decrease with the square of the distance from the source.
  • Wavelength of the green light (λ): This determines the frequency and energy of the photons.

With these parameters, we can use the following equations:

  1. Intensity (I):
    The intensity of light at a distance r from a point source is given by:

    I = P / (4πr²) 
    

    where:

    • I is the intensity in W/m²
    • P is the power of the lamp in W
    • r is the distance from the lamp in m
  2. Electric Field (E):
    The relationship between intensity and electric field strength for an electromagnetic wave is:

    I = (1/2)ε₀cE²
    

    where:

    • I is the intensity in W/m²
    • ε₀ is the permittivity of free space (approximately 8.854 x 10⁻¹² C²/Nm²)
    • c is the speed of light in vacuum (approximately 3 x 10⁸ m/s)
    • E is the electric field strength in V/m

Solving the problem:

  1. First, determine the intensity (I) using the power (P) and distance (r) from the lamp.
  2. Then, use the intensity (I) in the second equation to calculate the electric field strength (E).

Example:

Let's assume the lamp has a power of 10W and we want to find the electric field strength at a distance of 1m.

  1. I = 10W / (4π(1m)²) ≈ 0.796 W/m²
  2. 0.796 W/m² = (1/2)(8.854 x 10⁻¹² C²/Nm²)(3 x 10⁸ m/s)E²
    Solving for E, we get E ≈ 2.68 V/m

Therefore, without the necessary values for power and distance, a numerical solution cannot be provided. The solution would depend on these missing parameters.