Q.3 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 3 Solution

Topic: Moving Charges and Magnetism · Official NTA Booklet Code 45

Question

An electron (mass 9×10⁻³¹ kg and charge 1.6×10⁻¹⁹ C) moving with speed c/100 (c = speed of light) is injected into a magnetic field B of magnitude 9×10⁻⁴ T perpendicular to its direction of motion. We wish to apply an uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3×10⁸ m s⁻¹)

✓

Verified Against NTA Final Answer Key

Option (2) : \vec{E} \text{ is perpendicular to } \vec{B} \text{ and its magnitude is } 27 \times 10^2\text{ V m}^{-1}

📚 Moving Charges and Magnetism Easy

📋 Given Parameters & Problem Setup

Particle Electron (charge -e, mass m)

Speed (v) c / 100 = (3 × 10⁸) / 100 = 3 × 10⁶ m/s

Magnetic Field (B) 9 × 10⁻⁴ T (perpendicular to v)

Condition Undeflected straight-line motion

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The 30-Second Exam Hall Shortcut: ⚡ Velocity Selector Perpendicular Rule

⏱️ Save ~40 seconds

Crossed Fields: E ⟂ B, and E = vB = (3 × 10⁶) × (9 × 10⁻⁴) = 27 × 10² V/m!

1 Recall velocity selector condition: Magnetic force F_B = q(v × B) must be canceled by electric force F_E = qE.

2 For forces to be collinear and opposite, electric field E must be perpendicular to both velocity v and magnetic field B (i.e. E ⟂ B).

3 Calculate magnitude: E = v B = (3 × 10⁶ m/s) × (9 × 10⁻⁴ T) = 27 × 10² V/m.

4 Instantly eliminate parallel options (3) & (4), then match magnitude to Option (2).

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Why You Can 100% Trust This Shortcut: Lorentz Force Law (NCERT Physics · Moving Charges and Magnetism: F = q(v × B)).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Lorentz Force Balance Condition

For the electron to travel without any deflection, the net Lorentz force acting on it must be zero:

\vec{F}_{net} = q\left(\vec{E} + \vec{v} \times \vec{B}\right) = \vec{0} \implies \vec{E} = -(\vec{v} \times \vec{B})

• Because v and B are mutually perpendicular, the vector (v × B) is perpendicular to both v and B.
• Therefore, E must be strictly perpendicular to B.

Step 2

Magnitude Calculation

Equating the magnitudes of electric and magnetic forces gives the electric field magnitude required:

E = v B = \left(\frac{c}{100}\right) B = \left(3 \times 10^6\text{ m/s}\right) \times \left(9 \times 10^{-4}\text{ T}\right) = 27 \times 10^2\text{ V/m}

• Thus, E ⟂ B with magnitude 27 × 10² V/m (2700 V/m).

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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. Power of 10 error; used v = c instead of c/100.

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting to divide c by 100.

2 B

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. E ⟂ B and E = (3 × 10⁶)(9 × 10⁻⁴) = 27 × 10² V/m.

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Why this is airtight: None; textbook velocity selector.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. If E were parallel to B, electric force would be perpendicular to magnetic force and could never cancel it.

⚠️

Student Fallacy (Why candidates pick this trap): Misunderstanding the vector nature of cross products in Lorentz force.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Both direction (parallel) and magnitude (10⁴) are wrong.

⚠️

Student Fallacy (Why candidates pick this trap): Double mistake in orientation and speed scale.

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NTA Trap Alert: Parallel vs. Perpendicular Field Trap

Students often forget that crossed electric and magnetic fields MUST be mutually perpendicular (E ⟂ B ⟂ v) to achieve force cancellation. If E is parallel to B, the particle undergoes helical acceleration.

🛡️ How to avoid the -1 mark: Remember: Velocity Selector = CROSSED fields = E ⟂ B.

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Core NEET Syllabus Standard

NEET Physics Core Syllabus · Moving Charges and Magnetism Standard Benchmark

Core Scientific Principle Tested:

"Undeflected motion occurs when electric and magnetic forces are equal and opposite: E = vB with E ⟂ B."

Syllabus Focus: Motion in Combined Electric and Magnetic Fields

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Crossed Fields Cancel: E = vB and E ⟂ B!

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NEET 2025 Physics Question 3 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Velocity Selector Perpendicular Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Lorentz Force Balance Condition

Magnitude Calculation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Parallel vs. Perpendicular Field Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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