The electric field of an electromagnetic wave in free space is represented as E = E0 (omega t - kz)i The corresponding magnetic induction vector will be:

In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by E0 = c B0. Thus, B0 = E0 / C. The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors: C = E x B. Given the phase term (omega t - kz), the wave propagates in the +z direction, so C = k. The electric field oscillates in the +x direction, so E = i. We know: Since i x j = k, the magnetic field must oscillate in the +y direction (j). The full magnetic field vector shares the same phase and applies the above amplitude and direction: Phase remains identical. Amplitude scales by 1/c. Direction satisfies the right-hand triad (E, B, v) where v = E x B. Class 12 Physics: Electromagnetic Waves

The electric field of an electromagnetic wave in free space is represented as E = E0 (omega t - kz)i The corresponding magnetic induction vector will be:

In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by E0 = c B0. Thus, B0 = E0 / C. The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors: C = E x B. Given the phase term (omega t - kz), the wave propagates in the +z direction, so C = k. The electric field oscillates in the +x direction, so E = i. We know: Since i x j = k, the magnetic field must oscillate in the +y direction (j). The

The electric field of an electromagnetic wave in free space is represented as E = E0 (omega t - kz)i The corresponding magnetic induction vector will be:

In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by E0 = c B0. Thus, B0 = E0 / C. The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors: C = E x B. Given the phase term (omega t - kz), the wave propagates in the +z direction, so C = k. The electric field oscillates in the +x direction, so E = i. We know: Since i x j = k, the magnetic field must oscillate in the +y direction (j). The full magnetic field vector shares the same phase and applies the above amplitude and direction: Phase remains identical. Amplitude scales by 1/c. Direction satisfies the right-hand triad (E, B, v) where v = E x B. Class 12 Physics: Electromagnetic Waves

The electric field of an electromagnetic wave in free space is represented as E = E0 (omega t - kz)i The corresponding magnetic induction vector will be:

In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by E0 = c B0. Thus, B0 = E0 / C. The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors: C = E x B. Given the phase term (omega t - kz), the wave propagates in the +z direction, so C = k. The electric field oscillates in the +x direction, so E = i. We know: Since i x j = k, the magnetic field must oscillate in the +y direction (j). The

The electric field of an electromagnetic wave in free space is represented as E = E0 (omega t

Year	2026	2025	2024	Total
Questions	10	12	9	31

Year

2026

2025

2024

Total

Questions

Solution & Explanation

Related Formula

B₀ = (E₀)/(C)

C = E \times B

Core Logic

In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by $E₀ = c B₀$ $E_0 = c B_0$. Thus, $B₀ = E₀ / C$ $B_0 = E_0 / C$.

The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors: $C = E \times B$ $\hat{C} = \hat{E} \times \hat{B}$.

Step 1: Determine Wave Direction and Magnetic Field Direction

Given the phase term $(ω t - kz)$ $(\omega t - kz)$, the wave propagates in the $+z$ $+z$ direction, so $C = k$ $\hat{C} = \hat{k}$. The electric field oscillates in the $+x$ $+x$ direction, so $E = i$ $\hat{E} = \hat{i}$. We know:

k = i \times B

Since $i \times j = k$ $\hat{i} \times \hat{j} = \hat{k}$, the magnetic field must oscillate in the $+y$ $+y$ direction ( $j$ $\hat{j}$).

Step 2: Construct Final Vector

The full magnetic field vector shares the same phase and applies the above amplitude and direction:

B = (E₀)/(C) (ω t - kz) j

Pattern Recognition

Phase remains identical. Amplitude scales by $1/c$ $1/c$. Direction satisfies the right-hand triad $( E, B, v)$ $(\vec{E}, \vec{B}, \vec{v})$ where $v = E \times B$ $\vec{v} = \vec{E} \times \vec{B}$.

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Class 12 Physics: Electromagnetic Waves

More Electromagnetic Waves Previous-Year Questions — Page 7

Q40 jee_main_2024_31_jan_morning Energy Density Of EM Waves

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of

5 \times 10¹⁰ ~Hz

and an amplitude of

50 ~Vm⁻¹

. The total average energy density of the electromagnetic field of the wave is : [Use

ε₀ = 8.85 \times 10⁻¹² C² / Nm²

]

A. $1.106 \times 10⁻⁸ Jm⁻³$
B. $4.425 \times 10⁻⁸ ~Jm⁻³$
C. $2.212 \times 10⁻⁸ ~Jm⁻³$
D. $2.212 \times 10⁻¹⁰ ~Jm⁻³$

Solution

Related Formula

Utotal average = (1)/(2)ε₀ E₀²

Core Logic

For an electromagnetic wave, the total average energy density is the sum of the average energy density of the electric field and the magnetic field. They are equal, so:

Uavg = UE + UB = 2UE = 2 ( (1)/(4)ε₀ E₀² ) = (1)/(2)ε₀ E₀²

Where $E₀$ $E_0$ is the amplitude of the electric field.

Step 2: Substitution

Given: $E₀ = 50 V/m$ $E_0 = 50 \mathrm{\, V/m}$ $ε₀ = 8.85 \times 10⁻¹² C²/(N\cdot m²)$

Uavg = (1)/(2) \times (8.85 \times 10⁻¹²) \times (50)²

Uavg = (1)/(2) \times 8.85 \times 10⁻¹² \times 2500

Uavg = 1.10625 \times 10⁻⁸ J/m³

Chapter Mix

Class 12 Physics: Electromagnetic Waves

The electric field of an electromagnetic wave in free space is represented as $E = E₀ (ω t - kz) i$ The corresponding magnetic induction vector will be:

Solution & Explanation

Related Formula

Core Logic

Step 1: Determine Wave Direction and Magnetic Field Direction

Step 2: Construct Final Vector

Pattern Recognition

Chapter Mix

Reference Study Guides

More Electromagnetic Waves Previous-Year Questions — Page 7

Solution

Related Formula

Core Logic

Step 2: Substitution

Chapter Mix

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The electric field of an electromagnetic wave in free space is represented as E = E₀ (ω t - kz) i$\vec{E} = E_0\cos (\omega t - kz)\hat{i}$ The corresponding magnetic induction vector will be:

Solution & Explanation

Related Formula

Core Logic

Step 1: Determine Wave Direction and Magnetic Field Direction

Step 2: Construct Final Vector

Pattern Recognition

Chapter Mix

Reference Study Guides

More Electromagnetic Waves Previous-Year Questions — Page 7

Solution

Related Formula

Core Logic

Step 2: Substitution

Chapter Mix

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The electric field of an electromagnetic wave in free space is represented as $E = E₀ (ω t - kz) i$ The corresponding magnetic induction vector will be: