Physics · Electromagnetic Waves

JEE Main 2026 — 23 January, Morning Shift — Question 45

The equation of the electric field of an electromagnetic wave propagating through free space is given by: E=377sin⁡(6.27×103t−2.09×10−5x)N/C\mathrm{E}=\sqrt{377} \sin \left(6.27 \times 10^{3} \mathrm{t}-2.09 \times 10^{-5} \mathrm{x}\right) \mathrm{N} / \mathrm{C} he average power of the electromagnetic wave is (1α)W/m2\left(\frac{1}{\alpha}\right) \mathrm{W} / \mathrm{m}^{2}. The value of α\alpha is ____\_\_\_\_ (Take μ0ε0=377\sqrt{\frac{\mu_{0}}{\varepsilon_{0}}}=377 in SI units)

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

Here, v=ωK=6.27×1032.09×10−5\mathrm{v}=\frac{\omega}{\mathrm{K}}=\frac{6.27 \times 10^{3}}{2.09 \times 10^{-5}} =3×108=3 \times 10^{8} So, wave moving in vacuum Now, I=(12ε0E02)c=12ε0E021μ0ε0I=\left(\frac{1}{2} \varepsilon_{0} E_{0}^{2}\right) c=\frac{1}{2} \varepsilon_{0} E_{0}^{2} \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} =12ε0μ0E02=121377×377=\frac{1}{2} \sqrt{\frac{\varepsilon_{0}}{\mu_{0}}} \mathrm{E}_{0}^{2}=\frac{1}{2} \frac{1}{377} \times 377 1 d=12\frac{1}{\mathrm{~d}}=\frac{1}{2} d=2\mathrm{d}=2

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Subject
Physics
Chapter
Electromagnetic Waves
Topic
Power , Energy and Intensity of EM Waves