Q.38 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 38 Solution

Topic: Electromagnetic Waves · Official NTA Booklet Code 50

Question

An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant εᵣ = 9, has the electric field Eₓ = E₀ sin(kz − 2π×10⁶ t) V m⁻¹ where E₀ is the amplitude and k is the wave vector. Among the following options, the incorrect choice is:

✓

Verified Against NTA Final Answer Key

Option (2) : Both Options (2) and (3) Accepted as Correct by NTA (Official Key: B,C)

📚 Electromagnetic Waves Challenging

📋 Given Parameters & Problem Setup

Medium Lossless dielectric with dielectric constant epsilon_r = 9 (relative permeability mu_r = 1)

Electric Field E_x = E_0 sin(kz - 2*pi*10^6 t) V/m

Wave Amplitude E_0

Angular Frequency omega = 2*pi*10^6 rad/s (frequency f = 10^6 Hz = 1 MHz)

Question Requirement Identify the INCORRECT statement among the given options

Official NTA Key B,C (both options 2 and 3 awarded marks)

⚡

The 30-Second Exam Hall Shortcut: ⚡ The Dual-Key Flaw Diagnostic (Why NTA Accepted Both 2 and 3)

⏱️ Essential exam-hall awareness of NTA multi-key questions.

Statements (2) and (3) are BOTH scientifically false!

1 Speed of wave in medium: v = c / sqrt(epsilon_r) = (3 * 10^8) / sqrt(9) = (3 * 10^8) / 3 = 10^8 m/s ==> Statement (1) is TRUE.

2 Direction of propagation: Phase is (kz - omega*t), so wave travels along +z ==> Statement (4) is TRUE.

3 Wavelength in medium: lambda = v / f = (10^8 m/s) / (10^6 Hz) = 100 m! But Statement (2) claims lambda = 300 m (which is vacuum wavelength!). Therefore Statement (2) is INCORRECT!

4 Magnetic field amplitude: E_0 / B_0 = v ==> B_0 = E_0 / v. Statement (3) writes B_y = (B_0 / v) sin(...), which has dimensionally WRONG units (divides B_0 by v again!). Therefore Statement (3) is ALSO INCORRECT!

5 Because the question asked for the INCORRECT choice, and both (2) and (3) are false, NTA officially accepted BOTH (2) and (3)!

🛡️

Why You Can 100% Trust This Shortcut: In a dielectric medium, speed reduces to v = c/n and wavelength reduces to lambda = lambda_0/n = 300/3 = 100 m. Furthermore, magnetic field amplitude is B_0 = E_0/v; the expression (B_0/v) violates dimensional homogeneity.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Determine Wave Speed and Verify Statement (1)

For a non-magnetic lossless dielectric with relative permittivity epsilon_r = 9 and mu_r = 1:

v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{c}{\sqrt{\mu_r \epsilon_r}} = \frac{3 \times 10^8}{\sqrt{1 \times 9}} = \frac{3 \times 10^8}{3} = 10^8\text{ m/s}

• The speed of the wave inside the medium is exactly 10^8 m/s.
• Statement (1) is factually TRUE (hence not the answer to an "incorrect choice" question).

Step 2

Evaluate Wavelength and Prove Statement (2) is INCORRECT

From the wave equation E_x = E_0 \sin(kz - \omega t), angular frequency is omega = 2*pi*10^6 rad/s, so frequency f is:

f = \frac{\omega}{2\pi} = \frac{2\pi \times 10^6}{2\pi} = 10^6\text{ Hz} = 1\text{ MHz}

• Wavelength inside the medium: \lambda_{\text{medium}} = \frac{v}{f} = \frac{10^8\text{ m/s}}{10^6\text{ Hz}} = 100\text{ m}.
• Statement (2) asserts that wavelength inside the medium is 300 m (which is the wavelength in free space c/f = 300 m).
• Therefore, Statement (2) is definitely INCORRECT.

Step 3

Evaluate Magnetic Field and Prove Statement (3) is ALSO INCORRECT

By Maxwell's equations, the relationship between peak amplitudes of E and B in a medium is:

\frac{E_0}{B_0} = v \implies B_0 = \frac{E_0}{v}

• The magnetic field must be B_y = B_0 \sin(kz - \omega t) = \left(\frac{E_0}{v}\right) \sin(kz - \omega t).
• Statement (3) mistakenly writes: B_y = \left(\frac{B_0}{v}\right) \sin(kz - \omega t), which divides B_0 by v again, producing incorrect units of [Tesla / (m/s)].
• Therefore, Statement (3) is ALSO factually and dimensionally INCORRECT.
• During answer key challenges, NTA accepted both challenges and declared BOTH Option (2) and Option (3) as correct answers (Key: B,C).

⭐

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 Option (1)

✗ Incorrect

Verdict & Scientific Reason:

This statement is scientifically TRUE (speed is indeed 10^8 m/s).

⚠️

Student Fallacy (Why candidates pick this trap): Marks this option thinking it is false.

Note: Question asks for the INCORRECT choice.

2 Option (2)

✓ 100% Correct

Verdict & Scientific Reason:

INCORRECT STATEMENT (Wavelength in medium is 100 m, not 300 m); officially accepted by NTA.

💡

Why this is airtight: Recognizes that 300 m is vacuum wavelength, not medium wavelength.

Note: Awarded full marks under official NTA key.

3 Option (3)

✓ 100% Correct

Verdict & Scientific Reason:

INCORRECT STATEMENT (Dimensionally flawed: amplitude is B_0, not B_0/v); officially accepted by NTA.

💡

Why this is airtight: Recognizes the dimensional error in the setter's magnetic field amplitude.

Note: Awarded full marks under official NTA key.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

This statement is scientifically TRUE (phase is kz - omega*t).

⚠️

Student Fallacy (Why candidates pick this trap): Confuses wave propagation direction with field oscillation axis.

Note: Question asks for the INCORRECT choice.

⚠️

NTA Trap Alert: The Free Space Wavelength Trap (300 m vs 100 m)

Many students compute lambda = c / f = 3*10^8 / 10^6 = 300 m and conclude that Statement (2) is true, forgetting that waves SLOW DOWN in dielectric media, compressing wavelength to lambda / n = 100 m.

🛡️ How to avoid the -1 mark: Always use medium velocity for wavelength in media: lambda = v / f = (c / n) / f.

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Electromagnetic Waves Standard Benchmark

Core Scientific Principle Tested:

"In a dielectric medium: v = c / sqrt(epsilon_r), lambda = v / f = lambda_0 / sqrt(epsilon_r), and E_0 / B_0 = v."

Syllabus Focus: Propagation of EM Waves in Dielectric Media & Field Relations

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 38 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ The Dual-Key Flaw Diagnostic (Why NTA Accepted Both 2 and 3)

Step-by-Step Rigorous Workflow & Mathematical Proof

Determine Wave Speed and Verify Statement (1)

Evaluate Wavelength and Prove Statement (2) is INCORRECT

Evaluate Magnetic Field and Prove Statement (3) is ALSO INCORRECT

360° Option Elimination Engine Key Feature

NTA Trap Alert: The Free Space Wavelength Trap (300 m vs 100 m)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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