Q.26 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 26 Solution

Topic: Electromagnetic Waves · Official NTA Booklet Code 45

Question

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is:

✓

Verified Against NTA Final Answer Key

Option (3) : non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates

📚 Electromagnetic Waves Medium

📋 Given Parameters & Problem Setup

Capacitor Geometry Circular parallel plates of radius R

Charging Rate Surface charge density σ(t) increases at a constant rate with time

Target Property Spatial variation of induced magnetic field B(r) arising from displacement current

⚡

The 30-Second Exam Hall Shortcut: ⚡ Ampère-Maxwell Cylindrical Peak Rule

⏱️ Save ~50 seconds

Inside plates (r ≤ R): B ∝ r (linear growth); Outside plates (r ≥ R): B ∝ 1/r (hyperbolic decay) ⟹ B is MAXIMUM at the perimeter (r = R)!

1 Displacement current density J_d = ε₀ (dE/dt) is uniform across the circular plates of radius R.

2 Inside the plates (r ≤ R): Ampèrian loop of radius r encloses flux ∝ r² ⟹ B(2πr) = μ₀ J_d (πr²) ⟹ B(r) ∝ r.

3 Outside the plates (r ≥ R): Ampèrian loop encloses the entire total displacement current I_d ⟹ B(2πr) = μ₀ I_d ⟹ B(r) ∝ 1/r.

4 Thus B(r) starts from 0 at the center (r = 0), increases linearly to a MAXIMUM at the rim (r = R), and then decays as 1/r outside.

5 Therefore, B is non-zero everywhere with its maximum at the cylindrical surface connecting the peripheries (r = R)!

6 Select Option (3) in under 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Ampère-Maxwell Law (NCERT Physics · Electromagnetic Waves: Displacement Current I_d = ε₀ dΦ_E/dt).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Displacement Current Density Between the Plates

For circular parallel plates of radius R, the electric field between the plates is E = σ / ε₀. Since dσ/dt is constant, the time derivative of the electric field is uniform:

\frac{dE}{dt} = \frac{1}{\varepsilon_0} \frac{d\sigma}{dt} = \text{constant}

• Displacement current density J_d = ε₀ (dE/dt) is uniform throughout the cylindrical region between the plates.

Step 2

Magnetic Field Inside the Plates (r ≤ R)

Construct a circular Ampèrian loop of radius r ≤ R coaxial with the plates. Applying the Ampère-Maxwell law:

\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{d,enclosed} \implies B(r) \cdot 2\pi r = \mu_0 \left( \varepsilon_0 \pi r^2 \frac{dE}{dt} \right) \implies B(r) = \frac{\mu_0 \varepsilon_0 r}{2} \frac{dE}{dt} \propto r

• The magnetic field grows linearly from zero on the central axis (r = 0) up to the edge r = R.

Step 3

Magnetic Field Outside the Plates (r ≥ R) & Maximum

For an Ampèrian loop of radius r ≥ R, the enclosed displacement current is the full total displacement current I_d = ε₀ π R² (dE/dt):

B(r) \cdot 2\pi r = \mu_0 I_d \implies B(r) = \frac{\mu_0 \varepsilon_0 R^2}{2r} \frac{dE}{dt} \propto \frac{1}{r}

• Because B increases for r ≤ R and decreases for r ≥ R, it attains its global maximum at r = R (the peripheral boundary).
• Thus B is non-zero everywhere and reaches maximum at the imaginary cylindrical surface connecting the peripheries, matching Option (3).

⭐

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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Maxwell discovered displacement current precisely because a changing electric field generates a non-zero magnetic field.

⚠️

Student Fallacy (Why candidates pick this trap): Believing that because no physical conduction electrons cross the vacuum gap, B must be zero.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. B grows linearly with r inside (B ∝ r) and decays as 1/r outside; it is neither constant nor zero outside.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing electric field (which is uniform) with induced magnetic field.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

100% exact. B(r) ∝ r for r ≤ R and B(r) ∝ 1/r for r ≥ R, peaking at r = R.

💡

Why this is airtight: None; canonical Maxwell-Ampère electrodynamics.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. B is non-zero throughout the interior except on the singular line r = 0.

⚠️

Student Fallacy (Why candidates pick this trap): Inverting spatial domains.

⚠️

NTA Trap Alert: Confusing Electric Field with Induced Magnetic Field

The electric field E between the plates is uniform (constant in space). But the INDUCED magnetic field B is created by enclosed displacement flux, so it grows with radius (B ∝ r) and peaks at the perimeter.

🛡️ How to avoid the -1 mark: Remember: E is uniform; B forms concentric loops that grow linearly to the edge!

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Electromagnetic Waves Standard Benchmark

Core Scientific Principle Tested:

"Magnetic field inside charging capacitor is B(r) ∝ r (r ≤ R) and B(r) ∝ 1/r (r ≥ R), peaking at r = R."

Syllabus Focus: Displacement Current & Ampère-Maxwell Law

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Inside: B grows with r; Outside: B dies as 1/r ⟹ PEAK at the rim (r = R)!

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 180-minute timed NTA simulator.

Launch NEET 2025 CBT Test →

← Previous (Q.25) All Physics Questions Grid Next (Q.27) →

🔗 Related Questions — Electromagnetic Waves

All 11 Electromagnetic Waves PYQs →

NEET 2026 Q38

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

View Solution →

NEET 2026 Q43

Spotted a mistake in this solution? Report an error (support@mycompetitiveexams.com)

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2025 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

NEET 2025 Physics Question 26 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Ampère-Maxwell Cylindrical Peak Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Displacement Current Density Between the Plates

Magnetic Field Inside the Plates (r ≤ R)

Magnetic Field Outside the Plates (r ≥ R) & Maximum

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Electric Field with Induced Magnetic Field

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Electromagnetic Waves

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

Matching Electromagnetic Spectrum Bands to Technological & Medical Applications

Displacement Current in a Charging Capacitor Gap

Properties of Electromagnetic Waves in Free Space

Solve 4 NEET Questions a Day — One per Subject