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A light bulb emits light uniformly in all directions. The average emitted power is 150. 0 W. At a distance of 7 m from the bulb, determine (a) the average intensity of the light, (b) the rms value of the electric field, and (c) the peak value of the electric field

User Phortuin
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Answer: To determine the average intensity of the light, the RMS value of the electric field, and the peak value of the electric field, we'll use the following formulas and relationships:

Average intensity (I_avg) is given by:

I_avg = P_avg / A

where P_avg is the average emitted power and A is the area of a sphere with radius r (distance from the bulb).

RMS value of the electric field (E_rms) is related to the intensity by:

E_rms = √(2 * μ₀ * I_avg)

where μ₀ is the permeability of free space (approximately 4π × 10^-7 T·m/A).

Peak value of the electric field (E_peak) is related to the RMS value by:

E_peak = √2 * E_rms

Let's proceed with the calculations:

Given data:

Average emitted power (P_avg) = 150.0 W

Distance from the bulb (r) = 7 m

(a) Average intensity (I_avg):

The area of a sphere with radius r is A = 4πr².

A = 4π * (7 m)² ≈ 4π * 49 m² ≈ 193.62 m²

I_avg = P_avg / A

I_avg = 150.0 W / 193.62 m² ≈ 0.774 W/m²

The average intensity of the light at a distance of 7 m from the bulb is approximately 0.774 W/m².

(b) RMS value of the electric field (E_rms):

μ₀ = 4π × 10^-7 T·m/A

E_rms = √(2 * μ₀ * I_avg)

E_rms = √(2 * 4π × 10^-7 T·m/A * 0.774 W/m²)

E_rms ≈ √(3.094 × 10^-7 T·m²/A·W)

Now, we need to convert the units of E_rms to volts per meter (V/m) since the electric field is typically represented in volts per meter.

1 T·m/A = 1 V·s/m² (by definition)

E_rms ≈ √(3.094 × 10^-7 V·s/m²·W)

E_rms ≈ √(3.094 × 10^-7 V²/m²)

E_rms ≈ √(3.094 × 10^-7) V/m

E_rms ≈ 5.55 × 10^-4 V/m

The RMS value of the electric field is approximately 5.55 × 10^-4 V/m.

(c) Peak value of the electric field (E_peak):

E_peak = √2 * E_rms

E_peak = √2 * 5.55 × 10^-4 V/m

E_peak ≈ 7.84 × 10^-4 V/m

The peak value of the electric field is approximately 7.84 × 10^-4 V/m.

User Heartmon
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