Q.172 Physics ⭐ 360° Option Elimination Active

NEET 2020 Physics Question 172 Solution

Topic: Moving Charges and Magnetism · Official NTA Booklet Code E1

Question

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is: (μ₀ = 4π×10⁻⁷ T m A⁻¹)

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Verified Against NTA Final Answer Key

Option (1) : 6.28 x 10^-4 T

📚 Moving Charges and Magnetism Easy

📋 Given Parameters & Problem Setup

Length of Solenoid (L) 50 cm = 0.5 m

Number of Turns (N) 100

Current (I) 2.5 A

Permeability (mu0) 4pi × 10^-7 T m A^-1

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The 30-Second Exam Hall Shortcut: ⚡ "n = N/L = 100/0.5 = 200 turns/m. B = mu0 n I = 4pi × 10^-7 × 200 × 2.5 = 2000pi × 10^-7 = 2pi × 10^-4 = 6.28 × 10^-4 T!"

⏱️ 20 seconds

The magnetic field inside a long solenoid is B = mu0 · n · I. The turn density is n = N / L = 100 / 0.5 m = 200 turns/m. Substituting gives B = (4pi × 10^-7) × 200 × 2.5 = 4pi × 10^-7 × 500 = 2000pi × 10^-7 = 2pi × 10^-4 = 6.28 × 10^-4 T. Takes under 10 seconds!

1 Compute turns per unit length:

n = \frac{N}{L} = \frac{100}{0.5\text{ m}} = 200\text{ m}^{-1}

2 Apply solenoid formula:

B = \mu_0 n I

3 Substitute:

B = (4\pi \times 10^{-7}) \times 200 \times 2.5 = (4\pi \times 10^{-7}) \times 500 = 2000\pi \times 10^{-7}\text{ T}

4 Simplify:

B = 2\pi \times 10^{-4} = 2 \times 3.14 \times 10^{-4} = 6.28 \times 10^{-4}\text{ T}

5 Select Option (1).

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Why You Can 100% Trust This Shortcut: NCERT Physics · Moving Charges and Magnetism (Magnetic Field of a Solenoid)

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for Magnetic Field of a Solenoid

By Ampere's circuital law, the magnetic field near the center inside a long current-carrying solenoid is uniform and given by: $B = \mu_0 n I$ , where $n$ is the number of turns per unit length.

Step 2

Convert Units and Calculate Turn Density

- Total turns: $N = 100$ - Length: $L = 50\text{ cm} = 0.5\text{ m}$ $n = \frac{N}{L} = \frac{100}{0.5} = 200\text{ turns/m}$ .

Step 3

Calculate Magnetic Field

$B = \mu_0 n I = (4\pi \times 10^{-7}\text{ T m A}^{-1}) \times (200\text{ m}^{-1}) \times (2.5\text{ A})$ $B = 4\pi \times 10^{-7} \times 500 = 2000\pi \times 10^{-7} = 2\pi \times 10^{-4}\text{ T}$ Substitute $\pi \approx 3.14$ : $B = 2 \times 3.14 \times 10^{-4} = 6.28 \times 10^{-4}\text{ T}$ .

Step 4

Match with Options

Matches Option 1.

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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

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value; B = mu0 n I = 4pi × 10^-7 × 200 × 2.5 = 6.28 × 10^-4 T.

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Why this is airtight: None; precise calculation.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; calculates the field at the end of the solenoid (B = 1/2 mu0 n I).

⚠️

Student Fallacy (Why candidates pick this trap): Using the end-of-solenoid formula instead of the center.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; forgot to convert 50 cm to 0.5 m, using L = 50 in the denominator.

⚠️

Student Fallacy (Why candidates pick this trap): Unit conversion error (cm to m).

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; both used end formula and made centimeter unit conversion error.

⚠️

Student Fallacy (Why candidates pick this trap): Compound error of formula and units.

⚠️

NTA Trap Alert: Centimeters to Meters & Center vs End

Length must be in meters: 50 cm = 0.5 m (turn density n = 100/0.5 = 200, not 100/50 = 2). Also, center is B = mu0 n I, while end is 1/2 mu0 n I.

🛡️ How to avoid the -1 mark: Always convert dimensions to SI units (meters) before applying electrodynamic formulas.

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Core NEET Syllabus Standard

Physics · Moving Charges and Magnetism Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: Magnetic Field at the Centre of a Long Solenoid

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Physics Question 172 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "n = N/L = 100/0.5 = 200 turns/m. B = mu0 n I = 4pi × 10^-7 × 200 × 2.5 = 2000pi × 10^-7 = 2pi × 10^-4 = 6.28 × 10^-4 T!"

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for Magnetic Field of a Solenoid

Convert Units and Calculate Turn Density

Calculate Magnetic Field

Match with Options

360° Option Elimination Engine Key Feature

NTA Trap Alert: Centimeters to Meters & Center vs End

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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