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Class 12  »  Physics  »  Moving Charges and Magnetism

Torque on a Current Loop - UNSOLVED PRACTICE SET

Class 12

Chapter: Moving Charges and Magnetism | Topic: Torque on a Current Loop

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Study Material.
Class 12

TORQUE ON A CURRENT LOOP - UNSOLVED PRACTICE SET

Topic: Torque on a Current Loop

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

Multiple Choice Questions

Q1. The torque on a current loop in a magnetic field is given by:

  1. τ = NIBA sin θ
  2. τ = NIBA cos θ
  3. τ = NIB/A sin θ
  4. τ = NIA/B sin θ

Q2. The torque on a current loop is maximum when:

  1. The plane of the loop is parallel to the field
  2. The plane of the loop is perpendicular to the field
  3. The normal to the loop is parallel to the field
  4. The current is zero

Q3. The magnetic moment of a current loop is given by:

  1. m = NIA
  2. m = NI/A
  3. m = N/IA
  4. m = IA/N

Q4. The SI unit of magnetic moment is:

  1. Ampere
  2. Ampere-meter²
  3. Tesla
  4. Weber

Q5. A current loop placed in a uniform magnetic field experiences:

  1. A net force but no torque
  2. A torque but no net force
  3. Both net force and torque
  4. Neither force nor torque

Q6. The work done in rotating a current loop from θ₁ to θ₂ in a magnetic field is:

  1. W = NIBA(θ₂ − θ₁)
  2. W = NIBA(cos θ₁ − cos θ₂)
  3. W = NIBA(sin θ₂ − sin θ₁)
  4. W = NIBA(θ₂² − θ₁²)

Short Answer Questions

Q7. Define magnetic moment of a current loop. Write its expression and SI unit.

Q8. A circular loop of radius 5 cm carrying current 2 A is placed in a uniform magnetic field of 0.3 T. Calculate the maximum torque on the loop.

Q9. Why does a current loop in a uniform magnetic field experience torque but not a net force? Explain.

Q10. A rectangular coil of 50 turns, dimensions 10 cm × 5 cm, carries current 3 A. Calculate its magnetic moment.

Q11. In which orientation of a current loop in a magnetic field is it in (a) stable equilibrium, and (b) unstable equilibrium?

Q12. A current loop is free to rotate in a uniform magnetic field. Explain why it aligns itself with the field.

Long Answer Questions

Q13. Derive the expression for the torque on a rectangular current loop placed in a uniform magnetic field. Show that τ = NIBA sin θ, where θ is the angle between the normal to the loop and the magnetic field.

Q14. Explain the analogy between a current loop and a bar magnet. How is the magnetic moment of a current loop similar to the magnetic moment of a bar magnet? Compare their behavior in a uniform magnetic field.

Q15. A circular coil of 100 turns and radius 8 cm carries current 5 A. It is placed in a uniform magnetic field B = 0.4 T.

(a) Calculate the magnetic moment of the coil.

(b) Calculate the maximum torque on the coil.

(c) Calculate the torque when the plane of the coil makes 30° with the field.

(d) Calculate the work done in rotating the coil from this position to the position of stable equilibrium.

Numerical / Application-Based Problems

Q16. In a school project, a student builds a simple DC motor using a rectangular coil with N = 50 turns, dimensions 6 cm × 4 cm. The coil carries current I = 2 A and is placed in a uniform magnetic field B = 0.5 T provided by permanent magnets.

(a) Calculate the magnetic moment of the coil.

(b) Calculate the maximum torque on the coil.

(c) The coil is mounted on an axle and can rotate. Explain why a commutator is needed for continuous rotation.

(d) Calculate the torque when the coil has rotated 45° from the position of maximum torque.

(e) If the student adds a second identical coil perpendicular to the first (forming a simple two-pole motor), how does the torque vary with angle? Sketch the graph.

Q17. A galvanometer coil has N = 200 turns, area A = 2 cm², and is suspended in a radial magnetic field B = 0.1 T by a torsion wire with restoring constant k = 10⁻⁸ N m/degree.

(a) Calculate the deflection in degrees when current I = 1 μA flows through the coil.

(b) Calculate the current sensitivity (deflection per unit current).

(c) If the coil resistance is 100 Ω, what is the voltage sensitivity?

(d) Explain why a radial magnetic field is preferred over a uniform field in galvanometers.

(e) A student suggests using a stronger magnetic field to increase sensitivity. What are the advantages and disadvantages?

Q18. A moving coil galvanometer has a rectangular coil with N = 100 turns, dimensions 2 cm × 1.5 cm. The coil is placed in a uniform magnetic field B = 0.2 T and is suspended by a phosphor-bronze strip with torsional constant C = 4 × 10⁻⁹ N m/degree. The coil resistance is G = 50 Ω.

(a) Calculate the deflection for a current of 10 μA.

(b) Calculate the figure of merit (current required for unit deflection).

(c) The galvanometer is to be converted into an ammeter of range 0–5 A. Calculate the shunt resistance required.

(d) The galvanometer is to be converted into a voltmeter of range 0–10 V. Calculate the series resistance required.

(e) Explain why the same galvanometer can be used for both purposes with different external resistances.


Total: 30 Marks | Time: 40 mins

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Magnetic Force on a Moving Charge Lorentz Force Motion of Charged Particle in Magnetic Field Cyclotron Magnetic Force on a Current Carrying Conductor Biot Savart Law Magnetic Field due to Straight Wire and Circular Loop Amperes Circuital Law Solenoid and Toroid Moving Coil Galvanometer Conversion to Ammeter and Voltmeter