What is the intensity in W/m2 of a 80 -W light bulb at a distance 10 cm from the bulb's center?
the surface area of the sphere is ... 4 π r^2
r = 10 cm = .1 m
intensity = 80 W / (4 * π * .01 m^2)
To find the intensity in watts per square meter (W/m^2) of a light bulb, we can use the inverse square law of light. The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source.
Given:
Power of the light bulb (P) = 80 W
Distance from the bulb's center (r) = 10 cm = 0.1 m
Step 1: Calculate the intensity at the bulb's center.
The intensity at the center is given by the formula:
Intensity = Power/Area
Since the area at the center is very small, we can assume it as a point source. Therefore, the intensity at the center will be the same as the power of the light bulb:
Intensity at the center = Power = 80 W
Step 2: Calculate the intensity at the given distance using the inverse square law.
The inverse square law states that the intensity is inversely proportional to the square of the distance:
Intensity = Intensity at the center / (distance^2)
Substituting the values:
Intensity = 80 W / (0.1 m)^2
Intensity = 80 W / 0.01 m^2
Intensity = 8000 W/m^2
Therefore, the intensity of an 80-W light bulb at a distance of 10 cm from the bulb's center is 8000 W/m^2.
To calculate the intensity in watts per square meter (W/m^2) of a light bulb at a given distance from its center, we can use the inverse square law of light radiation. The inverse square law states that the intensity of light is inversely proportional to the square of the distance.
The formula to calculate the intensity (I) is:
I = P / (4πr^2)
Where:
- I is the intensity in watts per square meter (W/m^2),
- P is the power of the light bulb in watts (W),
- r is the distance from the light source in meters (m),
- π is a mathematical constant (approximately 3.14159).
In this case, the power of the light bulb is 80 W and the distance from the bulb's center is 10 cm, which is equivalent to 0.1 meters.
Plugging these values into the formula:
I = 80 W / (4π * (0.1 m)^2)
Calculating further:
I = 80 W / (4π * 0.01 m^2)
Simplifying:
I = 80 W / (0.04π m^2)
I ≈ 636.62 W/m^2
Therefore, the intensity of an 80 W light bulb at a distance of 10 cm from the bulb's center is approximately 636.62 W/m^2.