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QPage 338: Q7: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Waves Page 338: Q7 Solution: A plane electromagnetic wave is passing through a region.…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume energy density oscillates at the same frequency as the electric and magnetic fields. Remember that energy density is proportional to the square of the field amplitude ($u \propto E^2$ or $B^2$), and the square of a sinusoidal function oscillates at twice the original frequency.

A plane electromagnetic wave is passing through a region. Consider a) electric field b) magnetic field c) electrical energy in a small volume and d) magnetic energy in a small volume. Construct the pairs of the quantities that oscillate with equal frequencies.

Step-by-Step Verified Solution

**Answer:** (a) and (b) oscillate with the same frequency as the wave. (c) and (d) oscillate with double the frequency of the wave. **Step-by-Step Explanation:** The electric field and magnetic field of a plane electromagnetic wave are sinusoidal functions of time, so they oscillate with the frequency of the wave. The energy densities are proportional to the squares of the fields (E_ and B_). Since the square of a sine function has a frequency double that of the original sine function, the electrical and magnetic energy densities oscillate with twice the frequency of the wave [citation:17].

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