Match List I with List II: List I List II A. B cdot dl = mu0 ic + mu0 0 (dphiE/dt) I. Gauss' law for electricity B. E cdot dl = -(dphiB/dt) II. Gauss' law for magnetism C. E cdot dA = (Q/0) III. Faraday law D. B cdot dA = 0 IV. Ampere - Maxwell law Choose the correct answer from the options given below:

Let's review the fundamental Maxwell's equations: 1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current: 2. **Faraday's Law of Induction** states that changing magnetic flux induces an electromotive force (EMF): 3. **Gauss's Law for Electricity** relates net electric flux to enclosed charge: 4. **Gauss's Law for Magnetism** states that magnetic monopoles do not exist: The match configurations are: * A arrow IV * B arrow III * C arrow I * D arrow II This perfectly corresponds to Option (3). Understand the integral geometries: Path integrals (line integrals cdot dl) correspond to circulating fields (induction laws like Ampere/Faraday). Surface integrals (flux integrals cdot dA) correspond to bounded charge states (Gauss laws). Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electrostatics Class 12 Physics: Magnetism and Matter

Match List I with List II: List I List II A. B cdot dl = mu0 ic + mu0 0 (dphiE/dt) I. Gauss' law for electricity B. E cdot dl = -(dphiB/dt) II. Gauss' law for magnetism C. E cdot dA = (Q/0) III. Farad

Let's review the fundamental Maxwell's equations: 1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current: 2. **Faraday's Law of Induction** states that changing magnetic flux induces an electromotive force (EMF): 3. **Gauss's Law for Electricity** relates net electric flux to enclosed charge: 4. **Gauss's Law for Magnetism** states that magnetic monopoles do not exist: The match configurations are: * A arrow IV * B arrow III * C arrow I * D

Match List I with List II: List I List II A. B cdot dl = mu0 ic + mu0 0 (dphiE/dt) I. Gauss' law for electricity B. E cdot dl = -(dphiB/dt) II. Gauss' law for magnetism C. E cdot dA = (Q/0) III. Faraday law D. B cdot dA = 0 IV. Ampere - Maxwell law Choose the correct answer from the options given below:

Let's review the fundamental Maxwell's equations: 1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current: 2. **Faraday's Law of Induction** states that changing magnetic flux induces an electromotive force (EMF): 3. **Gauss's Law for Electricity** relates net electric flux to enclosed charge: 4. **Gauss's Law for Magnetism** states that magnetic monopoles do not exist: The match configurations are: * A arrow IV * B arrow III * C arrow I * D arrow II This perfectly corresponds to Option (3). Understand the integral geometries: Path integrals (line integrals cdot dl) correspond to circulating fields (induction laws like Ampere/Faraday). Surface integrals (flux integrals cdot dA) correspond to bounded charge states (Gauss laws). Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electrostatics Class 12 Physics: Magnetism and Matter

Match List I with List II: List I List II A. B cdot dl = mu0 ic + mu0 0 (dphiE/dt) I. Gauss' law for electricity B. E cdot dl = -(dphiB/dt) II. Gauss' law for magnetism C. E cdot dA = (Q/0) III. Farad

Let's review the fundamental Maxwell's equations: 1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current: 2. **Faraday's Law of Induction** states that changing magnetic flux induces an electromotive force (EMF): 3. **Gauss's Law for Electricity** relates net electric flux to enclosed charge: 4. **Gauss's Law for Magnetism** states that magnetic monopoles do not exist: The match configurations are: * A arrow IV * B arrow III * C arrow I * D

Match List I with List II: List I List II A. B cdot dl = mu0 ic + mu0 0 (dphiE/dt) I. Gauss' law for electricity B. E…

Year	2026	2025	2024	Total
Questions	10	12	9	31

List I	List II
A. $\oint B \cdot d l = μ₀ ic + μ₀ ε₀ (dφE)/(dt)$	I. Gauss' law for electricity
B. $\oint E \cdot d l = -(dφB)/(dt)$	II. Gauss' law for magnetism
C. $\oint E \cdot d A = (Q)/(ε₀)$	III. Faraday law
D. $\oint B \cdot d A = 0$ $\oint \vec{B} \cdot d\vec{A} = 0$	IV. Ampere - Maxwell law

More Electromagnetic Waves Previous-Year Questions — Page 6

Q40 jee_main_2024_30_january_evening Momentum of EM Waves

If the total energy transferred to a surface in time

t

6.48 \times 10⁵ ~J

, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

A. $2.46 \times 10⁻³ ~kg ~m / s$
B. $2.16 \times 10⁻³ ~kg ~m / s$
C. $1.58 \times 10⁻³ ~kg ~m / s$
D. $4.32 \times 10⁻³ ~kg ~m / s$

Solution

Related Formula

p = (U)/(c)

Core Logic

For an electromagnetic wave incident on a surface that is completely absorbed, the total momentum transferred is equal to the total energy transferred divided by the speed of light in vacuum ( $c$ $c$).

Step 1: Calculate Momentum

Given total energy $E = 6.48 \times 10⁵ ~J$ $E = 6.48 \times 10^5 \mathrm{~J}$. Speed of light $c = 3 \times 10⁸ ~m/s$ $c = 3 \times 10^8 \mathrm{~m/s}$.

p = (E)/(c) = (6.48 \times 10⁵)/(3 \times 10⁸)

p = 2.16 \times 10⁻³ ~kg~m/s

Pattern Recognition

Always check for "complete absorption" versus "perfect reflection". For complete absorption, $p = E/c$ $p = E/c$. For perfect reflection, $p = 2E/c$ $p = 2E/c$.

Chapter Mix

Class 12 Physics: Electromagnetic Waves

Q49 jee_main_2024_30_january_evening Maxwell's Equations

Match List I with List II:

List-I	List-II
A. Gauss's law of magnetostatics	I. $\oint E \cdot d a = (1)/(ε₀) \int ρ dV$
B. Faraday's law of electro magnetic induction	II. $\oint B \cdot d a = 0$
C. Ampere's law	III. $\oint E \cdot d l = - ddt\int B \cdot d a$
D. Gauss's law of electrostatics	IV. $\oint B \cdot d l = μ₀ I$

Choose the correct answer from the options given below:

A. $A-I, B-III, C-IV, D-II$ $\text{A-I, B-III, C-IV, D-II}$
B. $A-III, B-IV, C-I, D-II$ $\text{A-III, B-IV, C-I, D-II}$
C. $A-IV, B-II, C-III, D-I$ $\text{A-IV, B-II, C-III, D-I}$
D. $A-II, B-III, C-IV, D-I$ $\text{A-II, B-III, C-IV, D-I}$

Solution

Core Logic

Match each law with its corresponding mathematical expression (Maxwell's equations). (A) Gauss's law of magnetostatics: The net magnetic flux through any closed surface is zero. $\oint B \cdot d a = 0$ (Matches II). (B) Faraday's law of electromagnetic induction: The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux. $\oint E \cdot d l = - ddt \int B \cdot d a$ (Matches III). (C) Ampere's law: The line integral of the magnetic field around a closed loop is proportional to the electric current passing through the loop. $\oint B \cdot d l = μ₀ I$ (Matches IV). (D) Gauss's law of electrostatics: The electric flux through any closed surface is proportional to the enclosed electric charge. $\oint E \cdot d a = (1)/(ε₀) \int ρ dV$ (Matches I).

Step 1: Final Match

A $arrow$ $\rightarrow$ II B $arrow$ $\rightarrow$ III C $arrow$ $\rightarrow$ IV D $arrow$ $\rightarrow$ I This matches option (4).

Pattern Recognition

These are the fundamental Maxwell equations in integral form. Memorizing their direct mappings guarantees quick marks.

Chapter Mix

Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electromagnetic Induction

Q38 jee_main_2024_30_jan_morning Properties of EM 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:

A. $B = E₀C (ω t - kz) j$
B. $B = (E₀)/(C) (ω t - kz) j$
C. $B = E₀C (ω t + kz) j$
D. $B = (E₀)/(C) (ω t + kz) j$

Solution

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 $v = E \times B$ $\vec{v} = \vec{E} \times \vec{B}$.

Chapter Mix

Class 12 Physics: Electromagnetic Waves

Q40 jee_main_2024_31_jan_evening Properties of EM Waves

Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface. In the light of the above statements, choose the most appropriate answer from the options given below:

A. Statement I is incorrect but Statement II is correct
B. Both Statement I and Statement II are correct
C. Both Statement I and Statement II are incorrect
D. Statement I is correct but Statement II is incorrect

Solution

Related Formula

ρE = (1)/(2)ε₀ Erms²

ρB = Brms²2μ₀

$pᵣ = (I)/(c)$ $$p_r = \frac{I}{c}$$ (radiation pressure for completely absorbing surface)

Core Logic

Statement I: In an EM wave, energy is stored in both the electric and magnetic fields. The energy densities are equal: $UE = UB$ $U_E = U_B$ because $E = cB$ $E = cB$ and $c² = (1)/(μ₀ ε₀)$ $c^2 = \frac{1}{\mu_0 \epsilon_0}$. This is a correct fact.

Statement II: Electromagnetic waves carry momentum ( $p = U/c$ $p = U/c$). When they strike a surface, they transfer this momentum, creating radiation pressure. This is also a correct fact.

Step 1: Final Evaluation

Since both facts are universally true theoretical properties of EM waves, both statements are correct.

Pattern Recognition

Standard NCERT theory. Energy density is strictly symmetric 50-50 between E and B. Momentum transfer $\to$ $\to$ pressure is the definitive signature of the particle-like nature (photons) of EM waves.

Chapter Mix

Class 12 Physics: Electromagnetic Waves

Solution & Explanation

Core Logic

Step 1: Match Evaluation

Pattern Recognition

Chapter Mix

Reference Study Guides

More Electromagnetic Waves Previous-Year Questions — Page 6

Solution

Related Formula

Core Logic

Step 1: Calculate Momentum

Pattern Recognition

Chapter Mix

Solution

Core Logic

Step 1: Final Match

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Determine Wave Direction and Magnetic Field Direction

Step 2: Construct Final Vector

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Final Evaluation

Pattern Recognition

Chapter Mix

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