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 3

Q2 jee_main_2025_24_jan_evening Electromagnetic Spectrum

Arrange the following in the ascending order of wavelength

(lambda)

: (A) Microwaves

(lambda_1)

(B) Ultraviolet rays

(lambda_2)

(lambda_3)

(D) X-rays

(lambda_4)

Choose the most appropriate answer from the options given below :

A. $lambda_4 < lambda_3 < lambda_2 < lambda_1$
B. $lambda_3 < lambda_4 < lambda_2 < lambda_1$
C. $lambda_4 < lambda_2 < lambda_3 < lambda_1$
D. $lambda_4 < lambda_3 < lambda_1 < lambda_2$

Solution

### Core Logic The order of components in the electromagnetic spectrum in increasing order of wavelength (

lambda

) is:

gammatext-rays < textX-rays < textU.V. rays < textVisible rays < textIR rays < textMicrowaves < textRadio waves

Given components: - Microwaves:

lambda_1

- Ultraviolet rays:

lambda_2

- Infrared rays:

lambda_3

- X-rays:

lambda_4

Comparing these yields:

lambda_4 < lambda_2 < lambda_3 < lambda_1

### Pattern Recognition Remember the mnemonic for the EM spectrum in increasing wavelength: "Good Xylophones Use Very Interesting Micro Radios" (Gamma, X-ray, UV, Visible, IR, Microwave, Radio). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electromagnetic Waves

Q19 jee_main_2025_28_jan_evening Electric and Magnetic Field Vectors

The magnetic field of an E.M. wave is given by

vecB=left(fracsqrt32hati+frac12hatjright)30~sinleft[omegaleft(t-fraczcright)right]

(S.I. Units). The corresponding electric field in S.I. units is:

A. $vecmathrmE = left(frac12hatmathrmi -fracsqrt32hatmathrmjright)30mathrmcsin left[omega left(mathrmt - fracmathrmzmathrmcright)right]$
B. $vecmathrmE = left(frac34\i +frac14hatmathrmjright)30mathrmccos left[omega left(mathrmt - fracmathrmzmathrmcright)right]$
C. $vecmathrmE = left(frac12hatmathrmi +fracsqrt32hatmathrmjright)30mathrmcsin left[omega left(mathrmt + fracmathrmzmathrmcright)right]$
D. $vecmathrmE = left(fracsqrt32hatmathrmi -frac12hatmathrmjright)30mathrmcsin left[omega left(mathrmt + fracmathrmzmathrmcright)right]$

Solution

### Related Formula For a plane electromagnetic wave propagating in a given direction: 1. Peak electric field amplitude relates to peak magnetic field amplitude via:

E_0 = B_0 cdot c

2. The directional orientation unit vectors satisfy the cross product relation:

hatE = hatB times hatc

where

hatc

points along the wave propagation vector direction. ### Core Logic Given the wave equation format, the phase term

left(t - fraczcright)

shows that propagation is along the positive z-axis :

hatc = hatk

The magnetic field direction unit vector is :

hatB = fracsqrt32hati + frac12hatj

Compute the electric field direction vector using the cross product relation :

hatE = hatB times hatk = left(fracsqrt32hati + frac12hatjright) times hatk

hatE = fracsqrt32(hati times hatk) + frac12(hatj times hatk)

Using unit vector properties (

hati times hatk = -hatj

and

hatj times hatk = hati

hatE = -fracsqrt32hatj + frac12hati = frac12hati - fracsqrt32hatj quad text

With peak amplitude

E_0 = 30c

, the resulting vector equation is:

vecE = left(frac12hati - fracsqrt32hatjright)30csinleft[omegaleft(t-fraczcright)right]

### Pattern Recognition The vectors

vecE

vecB

, and the propagation direction are always mutually perpendicular. Since

vecE cdot vecB = 0

, you can quickly double-check your answer by verifying that the \dot product of the final

vecE

and

vecB

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

Q jee_main_2025_29_jan_morning Properties of EM Waves

Given below are two statements : one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum. Reason (R): Mass of a photon is zero. In the light of the above statements, choose the most appropriate answer from the options given below:

A. (A) is true but (R) is false.
B. (A) is false but (R) is true.
C. Both (A) and (R) are true but (R) is not the correct explanation of (A).
D. Both (A) and (R) are true and (R) is the correct explanation of (A).

Solution

### Related Formula

p = fracEc

### Core Logic Assertion (A) is false because electromagnetic waves carry both energy and finite radiation momentum (

p = E/c

). Reason (R) is correct because the rest mass of a photon equals zero. ### Chapter Mix Class 12 Physics: Electromagnetic Waves

Q38 jee_main_2024_01_february_morning Displacement Current

A parallel plate capacitor has a capacitance

C = 200mathrm~pF

. It is connected to

230mathrm~V

ac supply with an angular frequency

300mathrm~rad/s

. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

A. $1.38mathrm~mu Atext and 1.38mathrm~mu A$
B. $14.3mathrm~mu Atext and 143mathrm~mu A$
C. $13.8mathrm~mu Atext and 138mathrm~mu A$
D. $13.8mathrm~mu Atext and 13.8mathrm~mu A$

Solution

### Related Formula Capacitive reactance:

X_C = frac1omega C

Conduction Current (

I_textrms

I_textrms = fracV_textrmsX_C = V_textrms cdot omega C

Continuity relation:

I_c = I_d

### Core Logic Given parameters:

C = 200mathrm~pF = 200 times 10^-12mathrm~F

V_textrms = 230mathrm~V

omega = 300mathrm~rad/s

. Calculate current:

I = V_textrms cdot omega C = 230 times 300 times 200 times 10^-12

### Step 1: Simplify Numerical Calculation

I = 230 times 60000 times 10^-12 = 13.8 times 10^-6mathrm~A = 13.8mathrm~mu A

By Maxwell's electromagnetic formulation, the displacement current

I_d

within the dielectric space matches the exterior conduction current

I_c

seamlessly in magnitude. ### Pattern Recognition Factual invariant: Conduction current always equals displacement current inside a standard layout loop context (

I_c = I_d

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

Q45 jee_main_2024_29_january_evening Electric and Magnetic Field Relations

A plane electromagnetic wave of frequency

35text MHz

travels in free space along the

X

-direction. At a particular point (in space and time)

vecE = 9.6hatjtext V/m

. The value of magnetic field at this point is:

A. $3.2 times 10^-8hatktext T$ $3.2 \times 10^{-8}\hat{k}\text{ T}$
B. $3.2 times 10^-8hatitext T$ $3.2 \times 10^{-8}\hat{i}\text{ T}$
C. $9.6hatjtext T$ $9.6\hat{j}\text{ T}$
D. $9.6 times 10^-8hatktext T$ $9.6 \times 10^{-8}\hat{k}\text{ T}$

Solution

### Related Formula The relation between the amplitudes of electric field

E

and magnetic field

B

in an EM wave is:

c = fracEB

where: *

c = 3 times 10^8text m/s

is the speed of light. The directions are related by the vector cross product:

hatE times hatB = hatv

where

hatv

is the direction of propagation of the EM wave. ### Core Logic Given: * Wave propagation direction,

hatv = hati

(along X-direction) * Electric field vector direction,

hatE = hatj

* Electric field magnitude,

E = 9.6text V/m

### Step 1: Calculate Magnetic Field Magnitude Using the magnitude relation:

B = fracEc = frac9.63 times 10^8 = 3.2 times 10^-8text T

### Step 2: Determine Magnetic Field Direction Using the direction cross-product rule:

hatE times hatB = hatv

hatj times hatB = hati

Since we know that

hatj times hatk = hati

, the direction of the magnetic field must be

hatk

hatB = hatk

Combining the magnitude and direction:

vecB = 3.2 times 10^-8hatktext T

### Pattern Recognition A propagation along

+x

with electric field along

+y

strictly mandates the magnetic field must point along

+z

(

+y times +z = +x

). This instantly eliminates Option 2 and Option 3, leaving only magnitude verification. ### 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.

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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.