91Ó°ÊÓ

The intensity of light, often denoted as \( I \), is a measure of how much energy a wave carries per unit area, per unit time. It is expressed in watts per square meter (W/m²). In the context of a light bulb, not all the provided power converts to visible light. For a 75 W light bulb, only 5% contributes to visible light. Therefore, calculating the visible light intensity involves determining how much of the bulb's power emerges in the visible spectrum.
The visible power \( P_{\text{visible}} \) is calculated as \( 0.05 \times 75 \, \text{W} = 3.75 \, \text{W} \).

Next, we use the surface area of the bulb (modeled as a sphere with a diameter of 6.0 cm) to find the intensity. The surface area \( A \) of a sphere is given by:

• Formula: \( A = 4 \pi r^2 \)
• Radius \( r = \frac{6.0 \, \text{cm}}{2} = 0.03 \, \text{m} \)
• \( A = 4 \pi (0.03 \, \text{m})^2 \approx 0.0113 \, \text{m}^2 \)

Finally, we calculate the intensity \( I \) using:

• Formula: \( I = \frac{P_{\text{visible}}}{A} \)
• \( I = \frac{3.75 \, \text{W}}{0.0113 \, \text{m}^2} \approx 331.86 \, \text{W/m}^2 \)

Thus, the intensity of visible light at the bulb's surface is approximately 331.86 W/m².

The electric field amplitude \( E_0 \) is a crucial aspect of electromagnetic waves, representing the strength of the electric field of the wave. This varies directly with the light wave's intensity. For electromagnetic waves, the intensity \( I \) is connected to the electric field amplitude by the equation:

• \( I = \frac{1}{2} c \varepsilon_0 E_0^2 \)
• \( c = 3 \times 10^8 \, \text{m/s} \), the speed of light
• \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \), the permittivity of free space

Given the intensity \( I = 331.86 \, \text{W/m}^2 \), we can solve for \( E_0 \):

• \( E_0 = \sqrt{\frac{2I}{c\varepsilon_0}} \)
• \( E_0 = \sqrt{\frac{2 \times 331.86}{3 \times 10^8 \times 8.85 \times 10^{-12}}} \approx 501.96 \, \text{V/m} \)

This calculation reveals that the electric field amplitude at the surface of the bulb is approximately 501.96 V/m, indicating the intensity of the electric component of the wave.

The magnetic field amplitude \( B_0 \) indicates the strength of the magnetic component of electromagnetic waves and is intrinsically linked to the electric field amplitude \( E_0 \). According to Maxwell's equations, these two components are interconnected through the speed of light \( c \). Therefore, given \( E_0 \), you can find \( B_0 \) using the simple relation:

• \( B_0 = \frac{E_0}{c} \)
• Substituting \( E_0 = 501.96 \, \text{V/m} \) and \( c = 3 \times 10^8 \, \text{m/s} \)
• \( B_0 = \frac{501.96 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \approx 1.673 \times 10^{-6} \, \text{T} \)

This result means that the magnetic field amplitude at the surface of the bulb measures approximately \(1.673 \times 10^{-6} \) T (tesla), capturing the wave's magnetic influence. Understanding the relationship between the electrical and magnetic fields is key to grasping how electromagnetic waves propagate through space.