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NEETPhysicsElectromagnetic Waves

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In an electromagnetic wave propagating in vacuum, the average energy density of the electric field is equal to the average energy density of the magnetic field. Reason (R): In vacuum, the amplitudes of the electric and magnetic fields are related by E₀ = cB₀ . In the light of the above statements,

Options

  1. ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
  2. BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
  3. C(A) is correct but (R) is not correct
  4. D(A) is not correct but (R) is correct

Correct answer

A. Both (A) and (R) are correct and (R) is the correct explanation of (A)

Step-by-step solution

The average energy density of the electric field is u_E = 1 4 ₀ E₀^2 . The average energy density of the magnetic field is u_B = B₀^2 4 ₀ . In vacuum, the speed of light is c = 1 ₀ ₀ , and the field amplitudes are related by E₀ = cB₀ . Substituting E₀ into the expression for u_E : u_E = 1 4 ₀ (cB₀)^2 = 1 4 ₀ ( 1 ₀ ₀ ) B₀^2 = B₀^2 4 ₀ = u_B . Thus, the average energy densities are equal, making the Assertion (A) correct. The Reason (R) is also correct and provides the exact mathematical relationship required to prov

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