Match List I with List II:
List-I List-II
A. Gauss's law of magnetostatics I. $oint vecE cdot mathrmdveca = frac1varepsilon_0 int rho mathrmdV$
B. Faraday's law of electro magnetic induction II. $oint vecB cdot mathrmdveca = 0$
C. Ampere's law III. $oint vecE cdot mathrmdvecl = -fracmathrmdmathrmdtint vecB cdot mathrmdveca$
D. Gauss's law of electrostatics IV. $oint vecB cdot mathrmdvecl = mu_0 I$
Choose the correct answer from the options given below:

List-I	List-II
A. Gauss's law of magnetostatics	I. $oint vecE cdot mathrmdveca = frac1varepsilon_0 int rho mathrmdV$
B. Faraday's law of electro magnetic induction	II. $oint vecB cdot mathrmdveca = 0$
C. Ampere's law	III. $oint vecE cdot mathrmdvecl = -fracmathrmdmathrmdtint vecB cdot mathrmdveca$
D. Gauss's law of electrostatics	IV. $oint vecB cdot mathrmdvecl = mu_0 I$

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

Solution & Explanation

### 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 vecB cdot mathrmdveca = 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 vecE cdot mathrmdvecl = -fracmathrmdmathrmdt int vecB cdot mathrmdveca

(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 vecB cdot mathrmdvecl = mu_0 I

(Matches IV). (D) Gauss's law of electrostatics: The electric flux through any closed surface is proportional to the enclosed electric charge.

oint vecE cdot mathrmdveca = frac1varepsilon_0 int rho mathrmdV

(Matches I). ### Step 1: Final Match A

rightarrow

II B

rightarrow

III C

rightarrow

IV D

rightarrow

I This matches option (4). ### Pattern Recognition These are the fundamental Maxwell equations in integral form. Memorizing their direct mappings guarantees quick marks. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electromagnetic Induction

Reference Study Guides

Electromagnetic Waves

More Electromagnetic Waves Previous-Year Questions — Page 4

Q40 jee_main_2024_29_jan_morning Maxwell Equations

Match List I with List II:

List I	List II
A. $oint vecB cdot dvecl = mu_0 i_c + mu_0 varepsilon_0 fracdphi_Edt$	I. Gauss' law for electricity
B. $oint vecE cdot dvecl = -fracdphi_Bdt$	II. Gauss' law for magnetism
C. $oint vecE cdot dvecA = fracQvarepsilon_0$	III. Faraday law
D. $oint vecB cdot dvecA = 0$ $\oint \vec{B} \cdot d\vec{A} = 0$	IV. Ampere - Maxwell law

Choose the correct answer from the options given below:

A. A-IV, B-I, C-III, D-II
B. A-II, B-III, C-I, D-IV
C. A-IV, B-III, C-I, D-II
D. A-I, B-II, C-III, D-IV

Solution

### Core Logic Let's review the fundamental Maxwell's equations: 1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current:

oint vecB cdot dvecl = mu_0 i_c + mu_0 varepsilon_0 fracdphi_Edt implies textA - IV

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

oint vecE cdot dvecl = -fracdphi_Bdt implies textB - III

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

oint vecE cdot dvecA = fracQvarepsilon_0 implies textC - I

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

oint vecB cdot dvecA = 0 implies textD - II

### Step 1: Match Evaluation The match configurations are: * A

rightarrow

IV * B

rightarrow

III * C

rightarrow

I * D

rightarrow

II This perfectly corresponds to Option (3). ### Pattern Recognition Understand the integral geometries: Path integrals (line integrals

oint cdot dvecl

) correspond to circulating fields (induction laws like Ampere/Faraday). Surface integrals (flux integrals

oint cdot dvecA

) correspond to bounded charge states (Gauss laws). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves Class 12 Physics: Electrostatics Class 12 Physics: Magnetism and Matter

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 10^5 mathrm~J

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

A. $2.46 times 10^-3 mathrm~kg mathrm~m / mathrms$
B. $2.16 times 10^-3 mathrm~kg mathrm~m / mathrms$
C. $1.58 times 10^-3 mathrm~kg mathrm~m / mathrms$
D. $4.32 times 10^-3 mathrm~kg mathrm~m / mathrms$

Solution

### Related Formula

p = fracUc

### 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

). ### Step 1: Calculate Momentum Given total energy

E = 6.48 times 10^5 mathrm~J

. Speed of light

c = 3 times 10^8 mathrm~m/s

p = fracEc = frac6.48 times 10^53 times 10^8

p = 2.16 times 10^-3 mathrm~kg~m/s

### Pattern Recognition Always check for "complete absorption" versus "perfect reflection". For complete absorption,

p = E/c

. For perfect reflection,

p = 2E/c

. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

Q38 jee_main_2024_30_jan_morning Properties of EM Waves

The electric field of an electromagnetic wave in free space is represented as

vecE = E_0cos (omega t - kz)hati

The corresponding magnetic induction vector will be:

A. $vecB = E_0Ccos (omega t - kz)hatj$
B. $vecB = fracE_0C cos (omega t - kz) hatj$
C. $vecB = E_0Ccos (omega t + kz)hatj$
D. $vecB = fracE_0Ccos (omega t + kz)hatj$

Solution

### Related Formula

B_0 = fracE_0C

hatC = hatE times hatB

### Core Logic In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by

E_0 = c B_0

. Thus,

B_0 = E_0 / C

. The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors:

hatC = hatE times hatB

. ### Step 1: Determine Wave Direction and Magnetic Field Direction Given the phase term

(omega t - kz)

, the wave propagates in the

+z

direction, so

hatC = hatk

. The electric field oscillates in the

+x

direction, so

hatE = hati

. We know:

hatk = hati times hatB

Since

hati times hatj = hatk

, the magnetic field must oscillate in the

+y

direction (

hatj

). ### Step 2: Construct Final Vector The full magnetic field vector shares the same phase and applies the above amplitude and direction:

vecB = fracE_0C cos(omega t - kz) hatj

### Pattern Recognition Phase remains identical. Amplitude scales by

1/c

. Direction satisfies the right-hand triad

(vecE, vecB, vecv)

where

vecv = vecE times vecB

. ### Evaluation Rubric / Model Answer null ### 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

rho_E = frac12varepsilon_0 E_rms^2

rho_B = fracB_rms^22mu_0

p_r = fracIc

(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:

U_E = U_B

because

E = cB

and

c^2 = frac1mu_0 epsilon_0

. This is a correct fact. Statement II: Electromagnetic waves carry momentum (

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

pressure is the definitive signature of the particle-like nature (photons) of EM waves. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

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