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MCQEasyJEE 2023Characteristics of EM Waves

JEE Physics 2023 Question with Solution

For the plane electromagnetic wave given by E=E0sin⁡(ωt−kx)E = E_0 \sin(\omega t - kx) and B=B0sin⁡(ωt−kx)B = B_0 \sin(\omega t - kx), the ratio of average electric energy density to average magnetic energy density is:

  • A

    22

  • B

    12\frac{1}{2}

  • C

    11

  • D

    44

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A plane electromagnetic wave with E=E0sin⁡(ωt−kx)E = E_0 \sin(\omega t - kx) and B=B0sin⁡(ωt−kx)B = B_0 \sin(\omega t - kx).

Find: The ratio of average electric energy density to average magnetic energy density.

By theory of electromagnetic waves,

UE=12ϵ0E2U_E = \frac{1}{2}\epsilon_0 E^2

and

UB=12μ0B2U_B = \frac{1}{2}\mu_0 B^2

For a plane electromagnetic wave, the average electric energy density and average magnetic energy density are equal.

Therefore, the ratio of average electric energy density to average magnetic energy density is 11.

The correct option is C.

Common mistakes

  • Using instantaneous field values without recalling the standard result for a plane electromagnetic wave. In such a wave, average electric and magnetic energy densities are equal. Use that relation before comparing the two quantities.

  • Confusing the magnetic energy density expression. Writing UBU_B with the wrong dependence on BB leads to an incorrect ratio. Use the correct formula for magnetic energy density exactly as given in electromagnetic wave theory.

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