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Field of a solenoid and circular loop: Class 12 practice

Inside a long solenoid B = μ₀nI where n is turns per metre. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Scientific notation

The idea behind field of a solenoid and circular loop

Inside a long solenoid B = μ₀nI where n is turns per metre. At the centre of a circular coil of N turns and radius R, B = μ₀NI/(2R). μ₀ = 4π × 10⁻⁷ T m/A.

Step-by-step method

  1. Find n (turns ÷ length) or N and R.
  2. Substitute into the formula.
  3. Give B in tesla (or mT).

Worked example 1 (Basic)

A solenoid 0.5 m long has 900 turns and carries 6 A. Find the field inside.

  1. n = 900/0.5 = 1800 per m
  2. B = μ₀nI = 13.572 mT
  3. Answer: 13.572 mT

Worked example 2 (Standard)

A solenoid 0.7 m long has 900 turns and carries 4 A. Find the field inside.

  1. n = 900/0.7 = 1285.7142857142858 per m
  2. B = μ₀nI = 6.463 mT
  3. Answer: 6.463 mT

Worked example 3 (Challenge)

A circular coil of 187 turns and radius 20 cm carries 8 A. Find the field at its centre.

  1. B = μ₀NI/2R
  2. = 4.700 mT
  3. Answer: 4.700 mT

Common mistakes and misconceptions

  • Using total turns instead of turns per metre
  • Using diameter for R

Practice questions

  1. (Basic) A solenoid 0.7 m long has 400 turns and carries 8 A. Find the field inside.
  2. (Basic) A solenoid 0.3 m long has 1000 turns and carries 4 A. Find the field inside.
  3. (Standard) A solenoid 0.4 m long has 600 turns and carries 2 A. Find the field inside.
  4. (Standard) A solenoid 0.9 m long has 700 turns and carries 8 A. Find the field inside.
  5. (Challenge) A circular coil of 195 turns and radius 5 cm carries 2 A. Find the field at its centre.
  6. (Challenge) A circular coil of 195 turns and radius 6 cm carries 2 A. Find the field at its centre.

Answer key with full working

  • Q1: n = 400/0.7 = 571.4285714285714 per m → B = μ₀nI = 5.745 mT → Answer: 5.745 mT
  • Q2: n = 1000/0.3 = 3333.3333333333335 per m → B = μ₀nI = 16.755 mT → Answer: 16.755 mT
  • Q3: n = 600/0.4 = 1500 per m → B = μ₀nI = 3.770 mT → Answer: 3.770 mT
  • Q4: n = 700/0.9 = 777.7777777777777 per m → B = μ₀nI = 7.819 mT → Answer: 7.819 mT
  • Q5: B = μ₀NI/2R → = 4.901 mT → Answer: 4.901 mT
  • Q6: B = μ₀NI/2R → = 4.084 mT → Answer: 4.084 mT

Syllabus note

This skill is listed under "Moving Charges and Magnetism" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is field of a solenoid and circular loop in?

"Moving Charges and Magnetism", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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