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I=(P)/(4pi r^(2)) At a large distance ...

`I=(P)/(4pi 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)=(IP)/(4pi)`

B

`r^(2)=(P)/(4pi I)`

C

`r^(2)=(4pi I)/(P)`

D

`r^(2)=(I)/(4pi P)`

Text Solution

Verified by Experts

Choice B is correct. To rearrange the formula `I=(P)/(4pi r^(2))` in terms of `r^(2)`, first multiply each side of the equation by `r^(2)`. This yields `r^(2)I=(P)/(4pi)`. Then dividing each side of `r^(2)I=(P)/(4pi)` by I gives `r^(2)=(P)/(4pi I)`.
Choices A, C, and D are incorrect and may result from algebraic errors during the rearrangement of the formula.
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