A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

Question

Quantrex Academy · Accepted Answer

Correct answer: C. decrease by 4 times

For a point source, intensity is given by

I = \frac{P}{4\pi r^2}

where

P

is power and

r

is distance.
If the volume of the spherical detector increases by 8 times, then

\frac{4}{3}\pi r_{new}^3 = 8 \cdot \frac{4}{3}\pi r_{old}^3

, giving

r_{new} = 2r_{old}

.
The new intensity is

I_{new} = \frac{P}{4\pi (2r_{old})^2} = \frac{1}{4} \cdot \frac{P}{4\pi r_{old}^2} = \frac{I_{old}}{4}

.
Therefore intensity decreases by 4 times.

A point source is kept at the center of a spherically enclosed...