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

Year

2026

2025

2024

Total

Questions

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

List I

List II

\oint B \cdot d l = μ₀ ic + μ₀ ε₀ (dφE)/(dt)

I. Gauss' law for electricity

\oint E \cdot d l = -(dφB)/(dt)

II. Gauss' law for magnetism

\oint E \cdot d A = (Q)/(ε₀)

III. Faraday law

\oint B \cdot d A = 0

IV. Ampere - Maxwell law

Solution & Explanation

Core Logic

Let's review the fundamental Maxwell's equations:

Ampere - Maxwell Law relates the magnetic path integral to conduction current and displacement current:

\oint B \cdot d l = μ₀ ic + μ₀ ε₀ (dφE)/(dt) A - IV

Faraday's Law of Induction states that changing magnetic flux induces an electromotive force (EMF):

\oint E \cdot d l = -(dφB)/(dt) B - III

Gauss's Law for Electricity relates net electric flux to enclosed charge:

\oint E \cdot d A = (Q)/(ε₀) C - I

Gauss's Law for Magnetism states that magnetic monopoles do not exist:

\oint B \cdot d A = 0 D - II

Step 1: Match Evaluation

The match configurations are:

A $arrow$ $\rightarrow$ IV
B $arrow$ $\rightarrow$ III
C $arrow$ $\rightarrow$ I
D $arrow$ $\rightarrow$ II

This perfectly corresponds to Option (3).

Pattern Recognition

Understand the integral geometries: Path integrals (line integrals $\oint \cdot d l$ $\oint \cdot d\vec{l}$) correspond to circulating fields (induction laws like Ampere/Faraday). Surface integrals (flux integrals $\oint \cdot d A$ $\oint \cdot d\vec{A}$) correspond to bounded charge states (Gauss laws).

Chapter Mix

Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electrostatics Class 12 Physics: Magnetism and Matter

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

Solution & Explanation

Core Logic

Step 1: Match Evaluation

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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Solution & Explanation

Core Logic

Step 1: Match Evaluation

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

More Electromagnetic Waves Questions — jee_main_2024_29_jan_morning

Select Your Target Exam

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