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JEE Main 20236 AprilEvening Shift
Exam
JEE Main
Year
2023
Date
6 April
Shift
Evening Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2023 · 6 April · Evening Shift · Physics · Electromagnetic Waves

The energy density associated with electric field → E and magnetic...

The energy density associated with electric field E→\overset{\to}{E} and magnetic field B→\overset{\to}{B} of an electromagnetic wave in free space is given by (ε0−{ε}_{0} - permittivity of free space, μ0−{\mu}_{0} - permeability of free space)

Options

  1. AUE=E22ε0,UB=B22μ0{U}_{E} = \dfrac{{E}^{2}}{2{ε}_{0}}, {U}_{B} = \dfrac{{B}^{2}}{2{\mu}_{0}}
  2. BUE=ε0E22,UB=B22μ0{U}_{E} = \dfrac{{ε}_{0}{E}^{2}}{2}, {U}_{B} = \dfrac{{B}^{2}}{2{\mu}_{0}}
  3. CUE=ε0E22,UB=μ0B22{U}_{E} = \dfrac{{ε}_{0}{E}^{2}}{2}, {U}_{B} = \dfrac{{\mu}_{0}{B}^{2}}{2}
  4. DUE=E22ε0,UB=μ0B22{U}_{E} = \dfrac{{E}^{2}}{2{ε}_{0}}, {U}_{B} = \dfrac{{\mu}_{0}{B}^{2}}{2}

Correct answer

B. UE=ε0E22,UB=B22μ0{U}_{E} = \dfrac{{ε}_{0}{E}^{2}}{2}, {U}_{B} = \dfrac{{B}^{2}}{2{\mu}_{0}}

Step-by-step solution

When an electromagnetic wave propagates from the source, it transfers energy to the objects in its path. Electric and magnetic fields serve as energy reservoirs for electromagnetic waves. An electromagnetic wave contains the same amount of energy as are contained in the electric and magnetic fields together. In such situation, the energy density of the electromagnetic wave is equal to the sum of the energies of the electric and magnetic fields.

The average electric and magnetic energy densities are given by

{UE=12ε0E2UB=12B2μ0\begin{cases}{U}_{E} & = & \dfrac{1}{2}{ε}_{0}{E}^{2} \\ {U}_{B} & = & \dfrac{1}{2}\dfrac{{B}^{2}}{{\mu}_{0}}\end{cases}

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