The electric field a plane electromagnetic wave is given by : The expression for magnetic field associated with this electromagnetic wave is ____ T.

The phase of the wave is (0.6 x 103 x - 1.8 x 1011 t). This indicates the wave propagates in the +x direction, so c = i. The electric field oscillates along the y-axis, so E = j. From B = c x E, we have B = i x j = k. So, the magnetic field is along the z-axis (Bz). Wave speed v = c = (omega/k) = 1.8 x 10110.6 x 103 = 3 x 108 m/s. The amplitude of the magnetic field is: The phase remains exactly the same as the electric field: B0 = E0/c gives the magnitude. The vector identity B = v x E gives the direction. Phase part never changes sign or terms between E and B equations. Class 12 Physics: Electromagnetic Waves

The electric field a plane electromagnetic wave is given by : The expression for magnetic field associated with this electromagnetic wave is ____ T.

The phase of the wave is (0.6 x 103 x - 1.8 x 1011 t). This indicates the wave propagates in the +x direction, so c = i. The electric field oscillates along the y-axis, so E = j. From B = c x E, we have B = i x j = k. So, the magnetic field is along the z-axis (Bz). Wave speed v = c = (omega/k) = 1.8 x 10110.6 x 103 = 3 x 108 m/s. The amplitude of the magnetic field is: The phase remains exactly the same as the electric field: B0 = E0/c gives the magnitude. The vector identity B = v x E gives th

The electric field a plane electromagnetic wave is given by : The expression for magnetic field associated with this electromagnetic wave is ____ T.

The phase of the wave is (0.6 x 103 x - 1.8 x 1011 t). This indicates the wave propagates in the +x direction, so c = i. The electric field oscillates along the y-axis, so E = j. From B = c x E, we have B = i x j = k. So, the magnetic field is along the z-axis (Bz). Wave speed v = c = (omega/k) = 1.8 x 10110.6 x 103 = 3 x 108 m/s. The amplitude of the magnetic field is: The phase remains exactly the same as the electric field: B0 = E0/c gives the magnitude. The vector identity B = v x E gives the direction. Phase part never changes sign or terms between E and B equations. Class 12 Physics: Electromagnetic Waves

The electric field a plane electromagnetic wave is given by : The expression for magnetic field associated with this electromagnetic wave is ____ T.

The phase of the wave is (0.6 x 103 x - 1.8 x 1011 t). This indicates the wave propagates in the +x direction, so c = i. The electric field oscillates along the y-axis, so E = j. From B = c x E, we have B = i x j = k. So, the magnetic field is along the z-axis (Bz). Wave speed v = c = (omega/k) = 1.8 x 10110.6 x 103 = 3 x 108 m/s. The amplitude of the magnetic field is: The phase remains exactly the same as the electric field: B0 = E0/c gives the magnitude. The vector identity B = v x E gives th

Solution & Explanation

### Related Formula

B_0 = fracE_0c

hatc = hatE times hatB

### Core Logic The phase of the wave is

(0.6 times 10^3 x - 1.8 times 10^11 t)

. This indicates the wave propagates in the

+x

direction, so

hatc = hati

. The electric field oscillates along the

y

-axis, so

hatE = hatj

. From

hatB = hatc times hatE

, we have

hatB = hati times hatj = hatk

. So, the magnetic field is along the

z

-axis (

B_z

). ### Step 1: Calculate Amplitude of B Wave speed

v = c = fracomegak = frac1.8 times 10^110.6 times 10^3 = 3 times 10^8text m/s

. The amplitude of the magnetic field is:

B_0 = fracE_0c = frac693 times 10^8 = 23 times 10^-8 = 2.3 times 10^-7text T

The phase remains exactly the same as the electric field:

B_z = 2.3 times 10^-7 sin(0.6 times 10^3 x - 1.8 times 10^11 t)

### Pattern Recognition

B_0 = E_0/c

gives the magnitude. The vector identity

hatB = hatv times hatE

gives the direction. Phase part never changes sign or terms between E and B equations. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

More Electromagnetic Waves Previous-Year Questions — Page 4

Q46 jee_main_2024_27_jan_morning Energy Density and Intensity

A plane electromagnetic wave propagating in x-direction is described by

E_y = (200text Vm^-1)sin[1.5 times 10^7t - 0.05x]

. The intensity of the wave is (Use

epsilon_0 = 8.85 times 10^-12text C^2textN^-1textm^-2

A. $35.4text Wm^-2$ $35.4\text{ Wm}^{-2}$
B. $53.1text Wm^-2$ $53.1\text{ Wm}^{-2}$
C. $26.6text Wm^-2$ $26.6\text{ Wm}^{-2}$
D. $106.2text Wm^-2$ $106.2\text{ Wm}^{-2}$

Solution

### Related Formula

I = frac12 epsilon_0 E_0^2 c

Where

E_0

is the amplitude of the electric field (

200text V/m

) and

c = 3 times 10^8text m/s

. ### Core Logic Substitute the constants into the equation:

I = frac12 times (8.85 times 10^-12) times (200)^2 times (3 times 10^8)

### Step 1: Compute value

I = frac12 times 8.85 times 10^-12 times 4 times 10^4 times 3 times 10^8

I = 2 times 8.85 times 3 times 10^0

I = 53.1text W/m^2

### Pattern Recognition Isolate powers of ten first (

10^-12 times 10^4 times 10^8 = 10^0

) to streamline intermediate tracking accuracy on calculation variables. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

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

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. $oint vecE cdot mathrmdveca = frac1varepsilon_0 int rho mathrmdV$
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:

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

### 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

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

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The electric field a plane electromagnetic wave is given by : $E_y = 69 sin [ 0.6 times 10^3 x - 1.8 times 10^11 t ]text V/m.$ The expression for magnetic field associated with this electromagnetic wave is ____ T.

Solution & Explanation

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The electric field a plane electromagnetic wave is given by : E_y = 69 sin [ 0.6 times 10^3 x - 1.8 times 10^11 t ]text V/m.$$E_y = 69 \sin [ 0.6 \times 10^3 x - 1.8 \times 10^{11} t ]\text{ V/m}.$$ The expression for magnetic field associated with this electromagnetic wave is ____ T.

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The electric field a plane electromagnetic wave is given by : $E_y = 69 sin [ 0.6 times 10^3 x - 1.8 times 10^11 t ]text V/m.$ The expression for magnetic field associated with this electromagnetic wave is ____ T.