JEE Physics Magnetism Force on Current-Carrying Conductor Torque on Loop

Magnetism — Force on Current-Carrying Conductor, Torque on Loop

What This Is and Why It Matters for JEE

Magnetism is a crucial topic in JEE, appearing in 2-3 questions every year. It's moderately difficult, with a mix of easy and tough questions. This topic is more important for JEE Advanced, where it's a key area of focus.

Prerequisites

• Electric Current: Understand the concept of electric current, its units, and the direction of current flow.
• Magnetic Field: Know the definition of a magnetic field, its units, and how to calculate it using the Biot-Savart law.
• Vector Algebra: Be familiar with vector addition, scalar product, and cross product.

Quick Revision Path

If you're rusty on these concepts, quickly review them before diving into magnetism.

Core Concepts (Exam-Focused)

• Force on Current-Carrying Conductor: The force on a current-carrying conductor in a magnetic field is given by F = BIL sin(θ), where F is the force, B is the magnetic field strength, I is the current, L is the length of the conductor, and θ is the angle between the conductor and the magnetic field.
• Torque on Loop: The torque on a current-carrying loop in a magnetic field is given by τ = nIAB sin(θ), where τ is the torque, n is the number of turns, I is the current, A is the area of the loop, and θ is the angle between the loop and the magnetic field.
• Unit Conventions: Use the SI unit system, where the magnetic field strength is measured in teslas (T) and the current is measured in amperes (A).

Step-by-Step Problem-Solving Strategy

1. Identify the given quantities and the unknown quantity.
2. Check if the conductor or loop is parallel or perpendicular to the magnetic field.
3. Apply the relevant formula: F = BIL sin(θ) or τ = nIAB sin(θ).
4. ⚠️ Avoid using the formula F = BIL without checking the angle between the conductor and the magnetic field.
5. Check for multiple cases or special conditions, such as the conductor being at an angle or the loop being in a non-uniform magnetic field.

Important Graphs / Diagrams

No specific graphs or diagrams are required for this topic.

Typical JEE Question Patterns

• Find the minimum value of...: Use the formula and check for the minimum value of the given quantity.
• Compare time periods...: Use the formula and compare the time periods for different cases.
• Determine the direction of...: Use the right-hand rule to determine the direction of the force or torque.

Common Mistakes & Exam Traps

• The mistake: F = BIL without checking the angle between the conductor and the magnetic field.
  • Why it happens: Rushing or misreading the problem.
  • How to avoid it: Check the angle between the conductor and the magnetic field before applying the formula.
  • Exam board insight: This mistake is penalized in JEE Advanced, where the angle between the conductor and the magnetic field is often critical.
• The mistake: τ = nIAB without checking the angle between the loop and the magnetic field.
  • Why it happens: Misunderstanding the formula or rushing the problem.
  • How to avoid it: Check the angle between the loop and the magnetic field before applying the formula.
  • Exam board insight: This mistake is penalized in JEE Main, where the angle between the loop and the magnetic field is often critical.

Time-Saving Shortcuts

• Use the formula F = BIL sin(θ) to find the force on a current-carrying conductor in a magnetic field.
• Use the formula τ = nIAB sin(θ) to find the torque on a current-carrying loop in a magnetic field.

Practice MCQs (Exam-Style)

Question 1: A current-carrying conductor is placed in a magnetic field with a strength of 2 T. The conductor has a length of 0.5 m and a current of 5 A. What is the force on the conductor if it is perpendicular to the magnetic field?

A) 10 N B) 20 N C) 25 N D) 50 N

Answer: C) 25 N Solution: Use the formula F = BIL sin(θ). Since the conductor is perpendicular to the magnetic field, sin(θ) = 1. Therefore, F = 2 T x 5 A x 0.5 m x 1 = 5 N x 5 = 25 N.
Common Wrong Answer: Option A) 10 N, which is half the correct answer.

Question 2: A current-carrying loop is placed in a magnetic field with a strength of 3 T. The loop has an area of 0.1 m^2 and a current of 10 A. What is the torque on the loop if it is at an angle of 30° to the magnetic field?

A) 0.3 Nm B) 0.6 Nm C) 1.0 Nm D) 1.5 Nm

Answer: B) 0.6 Nm Solution: Use the formula τ = nIAB sin(θ). Since the loop is at an angle of 30° to the magnetic field, sin(θ) = 0.5. Therefore, τ = 1 x 10 A x 0.1 m^2 x 3 T x 0.5 = 1.5 Nm x 0.4 = 0.6 Nm.
Common Wrong Answer: Option C) 1.0 Nm, which is half the correct answer.

Question 3: A current-carrying conductor is placed in a magnetic field with a strength of 4 T. The conductor has a length of 1 m and a current of 20 A. What is the force on the conductor if it is at an angle of 60° to the magnetic field?

A) 40 N B) 80 N C) 120 N D) 160 N

Answer: C) 120 N Solution: Use the formula F = BIL sin(θ). Since the conductor is at an angle of 60° to the magnetic field, sin(θ) = 0.866. Therefore, F = 4 T x 20 A x 1 m x 0.866 = 69.33 N x 1.73 = 120 N.
Common Wrong Answer: Option B) 80 N, which is half the correct answer.

Quick Revision Card (60-Second Summary)

• Force on Current-Carrying Conductor: F = BIL sin(θ)
• Torque on Loop: τ = nIAB sin(θ)
• Unit Conventions: SI unit system, where B is measured in T and I is measured in A.
• Right-Hand Rule: Use the right-hand rule to determine the direction of the force or torque.
• Check the Angle: Always check the angle between the conductor or loop and the magnetic field.

If You Get Stuck in Exam

• Write Partial Marks: Write down what you know and what you're unsure about. This can earn you partial marks.
• Eliminate Distractors: Eliminate options that are clearly incorrect or impossible.
• Skip and Return: If you're stuck on a question, skip it and return to it later with a fresh mind.

Related JEE Topics

• Electric Current: Understand the concept of electric current, its units, and the direction of current flow.
• Magnetic Field: Know the definition of a magnetic field, its units, and how to calculate it using the Biot-Savart law.
• Vector Algebra: Be familiar with vector addition, scalar product, and cross product.