Energy & Intensity

Energy density and Poynting vector.

Concept

Energy & Intensity is a foundational idea in this chapter. The defining relationship is:

$u = \tfrac{1}{2}\varepsilon_0 E^2, \quad I = \tfrac{1}{2}c\varepsilon_0 E_0^2$

Intensity decreases as 1/r² from a point source.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $u = \tfrac{1}{2}\varepsilon_0 E^2, \quad I = \tfrac{1}{2}c\varepsilon_0 E_0^2$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.