Question

A bulb of power 100 W that radiates light isotropically(equally in all directions) has dimensions so small compared to the distances in question that the source can be assumed to be a point source.

Find the intensity 10 m away from it?

• A. $\frac{1}{4\pi }W/m^2$
• B. $\frac{1}{\pi }W/m^2$
• C. $\frac{2}{\pi }W/m^2$
• D. $Noneofthese$

Answer 1

The correct option is A

$\frac{1}{4\pi }W/m^2$

Let’s take a point source, radiating 10 J of energy per second. Since it radiates equal energy in all direction which spreads uniformly therefore all the points on a sphere of radius r from the point source will receive the same energy per unit time.

Okay so let me see how that applies to this question.

We are given a source of 100 W i.e., the source radiates 100 J every second.

Cool!

On a sphere of radius 10 m from the point source the Energy received per second will be… 100 J.

I hope that’s clear till here.

Now the intensity at any point on this sphere is what we need to find.

Intensity =

$\frac{1}{Area}\left(\frac{Energy}{time}\right)$

$=\frac{Power}{Area}$

Area of sphere = $4\pi r^2$

$=4\pi (10{)}^2=400\pi$

Intensity = $=\frac{100}{400\pi }=\left(\frac{1}{4\pi }\right)W/m^2$