Q.17 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 17 Solution

Topic: Electromagnetic Waves · Official NTA Booklet Code M1

Question

For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

✓

Verified Against NTA Final Answer Key

Option (2) : (-j + k), (-j - k)

📚 Electromagnetic Waves Medium

📋 Given Parameters & Problem Setup

Wave Direction Positive x-direction (+i)

Condition 1 E ⟂ B (E · B = 0)

Condition 2 Poynting vector E × B must point along +i

⚡

The 30-Second Exam Hall Shortcut: ⚡ Cross Product Filter: E × B must be along +i

⏱️ Save ~25 seconds

The wave propagates along $+x$ ( $\hat{i}$ ), so $\vec{E} \times \vec{B}$ must point along $+\hat{i}$ , and $\vec{E} \cdot \vec{B} = 0$ . In Option (2): $(-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = \hat{j}\times\hat{k} - \hat{k}\times\hat{j} = \hat{i} - (-\hat{i}) = +2\hat{i}$ ! In all other options, $\vec{E}$ and $\vec{B}$ are parallel or antiparallel (cross product = 0)! Select Option (2)!

1 Universal EM wave rule: Wave propagation direction is given by the unit vector along

\vec{E} \times \vec{B}

2 Here, propagation is along

+\hat{i}

. Thus,

\vec{E} \times \vec{B} = C \hat{i}

with

C > 0

3 Test Option (1):

\vec{E} = \vec{B} = \hat{j} + \hat{k} \implies \vec{E} \times \vec{B} = \vec{0}

(False).

4 Test Option (2):

(-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = 2\hat{i}

(Points along

+\hat{i}

! True!).

5 Test Option (3): Antiparallel

\implies \vec{E} \times \vec{B} = \vec{0}

(False).

6 Test Option (4): Parallel

\implies \vec{E} \times \vec{B} = \vec{0}

(False).

7 Match Option (2).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Maxwell's equations and Poynting vector electrodynamics for transverse EM waves.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Fundamental Orthogonality Relations of Electromagnetic Waves

In a transverse plane electromagnetic wave propagating in free space: 1. The electric field vector $\vec{E}$ and magnetic field vector $\vec{B}$ are perpendicular to each other: $\vec{E} \cdot \vec{B} = 0$ . 2. Both $\vec{E}$ and $\vec{B}$ are perpendicular to the wave propagation direction $\hat{k} = \hat{i}$ (so they lie in the $y$ - $z$ plane). 3. The direction of energy flow (Poynting vector) is along $\vec{E} \times \vec{B}$ :

\hat{c} = \frac{\vec{E} \times \vec{B}}{|\vec{E} \times \vec{B}|} = +\hat{i}

Step 2

Evaluating the Vector Cross Product for Option (2)

For $\vec{E} = -\hat{j} + \hat{k}$ and $\vec{B} = -\hat{j} - \hat{k}$ : - Check orthogonality: $\vec{E} \cdot \vec{B} = (-1)(-1) + (1)(-1) = 1 - 1 = 0$ (orthogonal). - Compute cross product using standard cyclic unit vector rules ( $\hat{j} \times \hat{k} = \hat{i}$ , $\hat{k} \times \hat{j} = -\hat{i}$ ):

\vec{E} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & -1 & 1 \\ 0 & -1 & -1 \end{vmatrix} = \hat{i}\left[(-1)(-1) - (1)(-1)\right] = \hat{i}(1 + 1) = +2\hat{i}

Step 3

Refutation of Remaining Options

Options (1) and (4) have parallel vectors $\vec{E} \parallel \vec{B}$ , yielding $\vec{E} \times \vec{B} = \vec{0}$ . Option (3) has antiparallel vectors $\vec{E} = -\vec{B}$ , also yielding $\vec{E} \times \vec{B} = \vec{0}$ . None of these can propagate an electromagnetic wave.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Electric and magnetic fields are parallel ( $\vec{E} \times \vec{B} = \vec{0}$ ), violating transversality and zero Poynting flux.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming

\vec{E}

and

\vec{B}

can point in the exact same direction.

2 2

✓ 100% Correct

Verdict & Scientific Reason:

Both vectors are mutually perpendicular ( $\vec{E} \cdot \vec{B} = 0$ ) and their cross product $\vec{E} \times \vec{B} = +2\hat{i}$ points along the positive $x$ -direction.

💡

Why this is airtight: None; rigorous vector cross product analysis.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Vectors are antiparallel ( $\vec{E} \times \vec{B} = \vec{0}$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Confusing opposite signs with perpendicular orientation.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Identical vectors with zero cross product.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming identical phase implies identical spatial orientation.

⚠️

NTA Trap Alert: Cyclic Vector Cross Product Sign Trap

Students frequently compute $\hat{k} \times \hat{j} = +\hat{i}$ instead of $-\hat{i}$ , flipping the resulting cross product to $-2\hat{i}$ and falsely eliminating the correct option.

🛡️ How to avoid the -1 mark: Use the standard determinant or cyclic rule:

\hat{i} \times \hat{j} = \hat{k}

\hat{j} \times \hat{k} = \hat{i}

\hat{k} \times \hat{j} = -\hat{i}

📖

Core NEET Syllabus Standard

NCERT Physics · Electromagnetic Waves Standard Benchmark

Core Scientific Principle Tested:

"In an electromagnetic wave, electric and magnetic fields are mutually perpendicular and perpendicular to the direction of propagation, with $\vec{S} \propto \vec{E} \times \vec{B}$ defining the wave vector."

Syllabus Focus: Transverse Nature of Electromagnetic Waves

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 17 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Cross Product Filter: E × B must be along +i

Step-by-Step Rigorous Workflow & Mathematical Proof

Fundamental Orthogonality Relations of Electromagnetic Waves

Evaluating the Vector Cross Product for Option (2)

Refutation of Remaining Options

360° Option Elimination Engine Key Feature

NTA Trap Alert: Cyclic Vector Cross Product Sign Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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EM Wave in Dielectric Medium: Dual-Key Question Audit (Both Options 2 and 3 Accepted by NTA)

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