Logo
Jeeify
MCQEasyJEE 2023Characteristics of EM Waves

JEE Physics 2023 Question with Solution

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

  • A

    22

  • B

    11

  • C

    33

  • D

    12\frac{1}{2}

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: An electromagnetic wave.

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

In an electromagnetic wave, the average electric energy density and average magnetic energy density are equal.

⟨uE⟩=⟨uB⟩\langle u_E \rangle = \langle u_B \rangle

The total average energy density is the sum of the two contributions.

⟨utotal⟩=⟨uE⟩+⟨uB⟩\langle u_{\text{total}} \rangle = \langle u_E \rangle + \langle u_B \rangle

Using ⟨uE⟩=⟨uB⟩\langle u_E \rangle = \langle u_B \rangle,

⟨utotal⟩=2⟨uE⟩\langle u_{\text{total}} \rangle = 2\langle u_E \rangle

Therefore,

⟨uE⟩⟨utotal⟩=12\frac{\langle u_E \rangle}{\langle u_{\text{total}} \rangle} = \frac{1}{2}

So, the required ratio is 12\frac{1}{2}. The correct option is D.

The solution labels the option inconsistently as C/Option 3, but the derived value 12\frac{1}{2} matches option D in the given options.

Equal Share Insight

Given: Electric and magnetic parts of an electromagnetic wave contribute equally to energy.

Find: The fraction due to electric energy alone in the total energy.

If total energy is shared equally between electric and magnetic fields, then the electric part is one out of two equal parts. Hence the ratio is 12\frac{1}{2}.

Therefore, the correct option is D.

Common mistakes

  • Assuming only the electric field stores energy. This is wrong because an electromagnetic wave has both electric and magnetic energy contributions. Add both parts to get the total energy density.

  • Using ⟨uE⟩=⟨utotal⟩\langle u_E \rangle = \langle u_{\text{total}} \rangle. This is incorrect because the total includes both ⟨uE⟩\langle u_E \rangle and ⟨uB⟩\langle u_B \rangle. Since they are equal, the electric part is half of the total.

Practice more Characteristics of EM Waves questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Characteristics of EM Waves

Related questions