Question

$I=\frac{P}{4\pi r^2}$
At a large distance $r$ from a radio antenna, the intensity of the radio signal $I$ is related to the power of the signal $P$ by the formula above.

Which of the following expresses the square of the distance from the radio antenna in terms of the

intensity of the radio signal and the power of the signal?

• A. $r^2=\frac{IP}{4\pi }$
• B. $r^2=\frac{P}{4\pi I}$
• C. $r^2=\frac{4\pi I}{P}$
• D. $r^2=\frac{I}{4\pi P}$

Answer 1

The correct option is B $r^2=\frac{P}{4\pi I}$

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

Since we need the square of distance from the radio antenna in terms of intensity, meaning $r^2$ in terms of $I$, we can write

$r^2=\frac{P}{4\pi I}$ bringing $r^2$ in numerator on the other side of equality and $I$ in the denominator.