Logo
Jeeify
MCQEasyJEE 2023Ampere's Law

JEE Physics 2023 Question with Solution

A long solenoid is formed by winding 70 turns cm−170 \, \text{turns cm}^{-1}. If 2.0 A2.0 \, \text{A} current flows, then the magnetic field produced inside the solenoid is:

  • A

    1232×10−4 T1232 \times 10^{-4} \, \text{T}

  • B

    176×10−4 T176 \times 10^{-4} \, \text{T}

  • C

    352×10−4 T352 \times 10^{-4} \, \text{T}

  • D

    88×10−4 T88 \times 10^{-4} \, \text{T}

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: A long solenoid has 70 turns cm−170 \, \text{turns cm}^{-1} and current I=2.0 AI = 2.0 \, \text{A}.

Find: The magnetic field inside the solenoid.

For a long solenoid, the magnetic field is

B=μ0nIB = \mu_0 n I

where μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7} \, \text{T m/A}.

Convert turns per centimetre into turns per metre:

n=70 cm−1=70×102 m−1n = 70 \, \text{cm}^{-1} = 70 \times 10^2 \, \text{m}^{-1}

Substitute the values:

B=(4π×10−7)(70×102)(2)B = (4\pi \times 10^{-7})(70 \times 10^2)(2) B=176×10−4 TB = 176 \times 10^{-4} \, \text{T}

Therefore, the magnetic field produced inside the solenoid is 176×10−4 T176 \times 10^{-4} \, \text{T}. The solution working gives this value, which matches option B, although the solution incorrectly labels the correct option as D.

Common mistakes

  • Using n=70 m−1n = 70 \, \text{m}^{-1} directly is wrong because the given winding density is per centimetre, not per metre. First convert 70 cm−170 \, \text{cm}^{-1} to 70×102 m−170 \times 10^2 \, \text{m}^{-1}.

  • Choosing option D only because the solution says 'The Correct Option is D' is wrong. The numerical working gives 176×10−4 T176 \times 10^{-4} \, \text{T}, so the defensible option is the one containing that value.

  • Forgetting the solenoid formula and using a wire or loop formula is wrong because this is a long solenoid. Use B=μ0nIB = \mu_0 n I for the field inside a long solenoid.

Practice more Ampere's Law questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Ampere's Law

Related questions