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Class 12  »  Physics  »  Moving Charges and Magnetism

Solenoid and Toroid - UNSOLVED PRACTICE SET

Class 12

Chapter: Moving Charges and Magnetism | Topic: Solenoid and Toroid

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Class 12

SOLENOID AND TOROID - UNSOLVED PRACTICE SET

Topic: Solenoid and Toroid

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. The magnetic field inside a long ideal solenoid is:

  1. Zero
  2. Uniform and parallel to the axis
  3. Non-uniform
  4. Perpendicular to the axis

Q2. The magnetic field inside a long solenoid carrying current I with n turns per unit length is:

  1. B = μ₀nI
  2. B = μ₀I/n
  3. B = μ₀n/I
  4. B = nI/μ₀

Q3. The magnetic field at the ends of a long solenoid is approximately:

  1. Equal to the field at the center
  2. Half the field at the center
  3. Twice the field at the center
  4. Zero

Q4. A toroid is essentially:

  1. A straight solenoid
  2. Option B
  3. A single circular loop
  4. A bar magnet

Q5. The magnetic field inside a toroid is:

  1. Zero
  2. Uniform and given by B = μ₀nI
  3. Non-uniform, varying with distance from the center
  4. Infinite

Q6. The magnetic field outside an ideal toroid is:

  1. Equal to the field inside
  2. Half the field inside
  3. Zero
  4. Very large

Short Answer Questions

Q7. Using Ampere's Circuital Law, derive the expression for the magnetic field inside a long solenoid.

Q8. A solenoid has 500 turns per meter and carries current 2 A. Calculate the magnetic field inside the solenoid.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q9. Why is the magnetic field outside an ideal toroid zero? Explain using Ampere's Circuital Law.

Q10. Distinguish between a solenoid and a toroid in terms of their magnetic field patterns.

Q11. A solenoid of length 50 cm has 1000 turns. What is the magnetic field at its center when carrying current 5 A?

Q12. Why does a solenoid behave like a bar magnet when current flows through it? Explain.

Long Answer Questions

Q13. Derive the expression for the magnetic field inside a long solenoid using Ampere's Circuital Law. Explain why the field is uniform inside and negligible outside. Draw a diagram showing the Amperian loop.

Q14. Derive the expression for the magnetic field inside a toroid using Ampere's Circuital Law. Show that the field varies inversely with the distance from the center of the toroid. Why is the field outside the toroid zero?

Q15. A solenoid has length l = 80 cm, radius r = 2 cm, and N = 2000 turns. It carries current I = 3 A.

(a) Calculate the magnetic field at the center of the solenoid.  

(b) Calculate the magnetic field at the ends of the solenoid.  

(c) Calculate the total number of turns per unit length.  

(d) If the solenoid is bent into a toroid of mean radius 15 cm, calculate the field at the mean radius.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Numerical / Application-Based Problems

Q16. In a school physics lab, a student builds an electromagnet using a solenoid. The solenoid has length 30 cm, diameter 4 cm, and is wound with 1200 turns of copper wire. It carries current I = 4 A.

(a) Calculate the magnetic field at the center of the solenoid.  

(b) Calculate the magnetic field at a point 5 cm from one end along the axis.  

(c) The student places an iron rod inside the solenoid. If the relative permeability of iron is μ_r = 1000, what is the new magnetic field?  

(d) Calculate the magnetic moment of the solenoid with the iron core.  

(e) Explain why electromagnets are preferred over permanent magnets in applications like cranes and doorbells.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q17. A toroid has inner radius r₁ = 15 cm, outer radius r₂ = 20 cm, and N = 800 turns. It carries current I = 5 A.

(a) Calculate the magnetic field at the inner edge, outer edge, and mean radius.  

(b) Calculate the percentage variation in the field from the inner to outer edge.  

(c) If the toroid is made with a ferromagnetic core (μ_r = 500), calculate the field at the mean radius.  

(d) Compare the toroid's field uniformity with that of a solenoid of the same length and turns.  

(e) Explain why toroids are used in transformers and inductors where confined magnetic fields are desired.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]

Q18. A superconducting solenoid used in an MRI machine has length l = 1 m, inner diameter 80 cm, and N = 2000 turns. It carries current I = 100 A and produces a field of 1.5 T.

(a) Verify that the theoretical field matches the given field. If not, explain the discrepancy.  

(b) Calculate the energy stored in the magnetic field inside the solenoid. [Hint: Energy density = B²/(2μ₀)]  

(c) If the superconducting wire has zero resistance, explain why the current persists indefinitely once established.  

(d) Calculate the inductance of the solenoid using L = μ₀N²A/l.  

(e) A quench (sudden loss of superconductivity) can be dangerous. Explain why, calculating the energy that would be dissipated as heat.

[Given: μ₀ = 4π × 10⁻⁷ T m/A]


Total: 30 Marks | Time: 40 mins

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