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Chapter 29: Problem 10

If you double the field strength in an electromagnetic wave, what happens to the intensity?

Short Answer

Expert verified
The intensity of the electromagnetic wave will increase four times if the field strength is doubled.

Step by step solution

01

Understanding the relationship between field strength and intensity

The relationship between field strength (E) and intensity (I) of an electromagnetic wave is given by the formula: \(I = c蔚_{0}E^{2}/2\), where c is the speed of light, \(蔚_{0}\) is the permittivity of free space, and E is the field strength.
02

Doubling the field strength

If we double the field strength, the new field strength will be 2E. Substituting this into the intensity formula, we'll get the new intensity \(I' = c蔚_{0}(2E)^{2}/2\).
03

Comparing the old and new intensities

On simplifying the expression for the new intensity, we find that \(I' = 4I\). This implies that when we double the field strength, the intensity increases by a factor of four.

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