At what distance does a 100 watt lightbulb deliver the same power per unit surface area as a 75 watt lightbulb produces 10 m away from the bulb? (assume both have the same efficiency for converting electrical energy in the circuit into emitted electromagnetic recall that watts = joules/second = power = energy per unit time. assume that the power of the electromagnetic waves spreads uniformly in all directions (i. e. spreads out over the area of a sphere) and use the formula for the surface area of a sphere.

At 11.5 m

Explanation:

The power per unit area corresponds to the intensity, which is given by

where

P is the power

is the area irradiated at a distance r from the source (it corresponds to the surface area of a sphere of radius r)

Here we want the intensity of the two light bulbs to be the same, so

where we have

P1 = 100 W is the power of the first light bulb

P2 = 75 W is the power of the second light bulb

r2 = 10 m is the distance from the second light bulb

Solving for r1, we find

if the person is shown to have +90n, then ans is -10n.

if the person is shown to have -90n, then ans is +10n.