Question

Power of a point source is 18 mW. Find the intensity 2.5 m away from the source.
A. 0.23\[mW/{{m}^{2}}\]
B. 9 \[mW/{{m}^{2}}\]
C. 0.23 \[W/{{m}^{2}}\]
D. 2.88 \[mW/{{m}^{2}}\]

Answer 1

Hint: In this question we have been asked to calculate the intensity of a wave at a distance of 2.5 m away from the source. We have been given that the power of the said point source is 18 mW. Now, we know that intensity is given as the power of point source transferred per unit area. Therefore, we shall be using this to calculate the intensity at said distance from the source.
Formula used:
 \[I=\dfrac{P}{A}\]
Where,
I is the intensity in \[W/{{m}^{2}}\]
P is the power in W, and
A is the area the power is carried through

Complete answer:
We know that power is the rate at which the energy is transferred by the wave. We also know that intensity is defined as the power transferred per unit area. Anything that is able to transmit energy is said to have intensity.
Now, we know that
\[I=\dfrac{P}{A}\] ……………… (1)
Now, for area we have been given that r = 2.5 m
Therefore,
\[A=4\pi {{r}^{2}}\]
After substituting the values
We get,
\[A=4\pi \times {{2.5}^{2}}\]
After substituting the above value in equation (1)
We get,
\[I=\dfrac{18\times {{10}^{-3}}}{4\pi \times {{2.5}^{2}}}\]
On solving,
\[I=2.29\times {{10}^{-3}}W/{{m}^{2}}\]
It can also be written as
\[I=2.23mW/{{m}^{2}}\]

So, the correct answer is “Option B”.

Note:
From the equation of intensity we can say that it is an example of inverse square law. If the energy radiated by the point source is not absorbed or scattered by any medium, then the intensity decreases inversely proportional to the square of distance from the source. Assuming that the medium in which the wave travels is damped the intensity will be lost quickly that the equation suggests. Intensity is basically the quantity of energy the wave transfers per unit time across a surface of unit area.