B = μ₀nI
F = IL × B
F = qv × B
τ = nIAB
μ = μ₀ × (n × I × A)
M = nIA
B = μ₀H + μ₀M
χ = (μ - 1)
μ = (1 + χ)
B = μ₀(H + M)
Magnetic field on axis of loop = μ₀I/(2r)
Magnetic field on perpendicular bisector of loop = μ₀I/(2πr³)³
Magnetic field due to solenoid = μ₀nI
Magnetic field due to toroid = μ₀nI/(2πr)
Force per unit length = μ₀I₁I₂/(2πr)

🪤 The 5 Mistakes That Cost Marks

Not using the correct formula for magnetic field due to a current carrying wire
Forgetting to consider the direction of magnetic field while calculating force on a current carrying wire
Not understanding the concept of magnetic moment and its relation to magnetic field
Incorrectly applying the formula for magnetic field due to a solenoid
Not considering the effect of magnetic field on a moving charge

✏️ 3 Solved PYQs

A current of 10 A is flowing ∈ a wire of length 1 m. The wire is placed ∈ a magnetic field of 0.1 T. If the angle between the wire and magnetic field is 30°, calculate the force acting on the wire.
- F = IL × B = 10 × 1 × 0.1 × s∈(30°) = 0.5 N
A solenoid of length 10 cm and radius 1 cm has 1000 turns. If a current of 5 A is flowing through it, calculate the magnetic field at its center.
- B = μ₀nI = 4π × 10⁻⁷ × 1000 × 5 = 0.0628 T
A bar magnet of magnetic moment 10 A m² is placed ∈ a magnetic field of 0.1 T. If the angle between the magnet and magnetic field is 60°, calculate the torque acting on the magnet.
- τ = MB s∈(θ) = 10 × 0.1 × s∈(60°) = 0.866 Nm

🧠 The One Thing Most Students Get Wrong

The concept of magnetic moment and its relation to magnetic field. Many students get confused between the two and end up using the wrong formula.

👁️ Ayush's Note

To solve problems related to magnetism, always start by identifying the given quantities and the unknown quantity.
Use the formula bank to find the relevant formula for the problem.
Always consider the direction of magnetic field and the angle between the wire and magnetic field while calculating force.
Practice problems regularly to develop a strong understanding of the concepts.

🔁 Last 5 Minutes Box

Revise the formula for magnetic field due to a current carrying wire.
Go through the concept of magnetic moment and its relation to magnetic field.
Practice a few problems related to force on a current carrying wire and magnetic field due to a solenoid.
Make sure to understand the concept of torque and its relation to magnetic moment.

📝 Practice MCQs

1. What is the magnetic field at the center of a solenoid of length 10 cm and radius 1 cm with 1000 turns, if a current of 5 A is flowing through it?

A) 0.01 T

B) 0.0628 T

C) 0.1 T

D) 1 T

Answer: B) 0.0628 T. Explanation: B = μ₀nI = 4π × 10⁻⁷ × 1000 × 5 = 0.0628 T

2. A current of 10 A is flowing ∈ a wire of length 1 m. The wire is placed ∈ a magnetic field of 0.1 T. If the angle between the wire and magnetic field is 30°, what is the force acting on the wire?

A) 0.1 N

B) 0.5 N

C) 1 N

D) 5 N

Answer: B) 0.5 N. Explanation: F = IL × B = 10 × 1 × 0.1 × s∈(30°) = 0.5 N

3. A bar magnet of magnetic moment 10 A m² is placed ∈ a magnetic field of 0.1 T. If the angle between the magnet and magnetic field is 60°, what is the torque acting on the magnet?

A) 0.5 Nm

B) 0.866 Nm

C) 1 Nm

D) 5 Nm

Answer: B) 0.866 Nm. Explanation: τ = MB s∈(θ) = 10 × 0.1 × s∈(60°) = 0.866 Nm

4. What is the magnetic field due to a current carrying loop of radius 1 m and current 5 A at a point on its axis at a distance of 2 m from its center?

A) 0.01 T

B) 0.0628 T

C) 0.1 T

D) 1 T

Answer: A) 0.01 T. Explanation: B = μ₀I/(2r) = 4π × 10⁻⁷ × 5/(2 × 2) = 0.01 T

5. A toroid of radius 10 cm and 1000 turns is carrying a current of 5 A. What is the magnetic field at its center?

A) 0.01 T

B) 0.0628 T

C) 0.1 T

D) 1 T

Answer: B) 0.0628 T. Explanation: B = μ₀nI/(2πr) = 4π × 10⁻⁷ × 1000 × 5/(2π × 0.1) = 0.0628 T

🚀 Ready to Ace Your Exam?

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🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

B = μ₀nI
F = IL × B
F = qv × B
τ = nIAB
μ = μ₀ × (n × I × A)
M = nIA
B = μ₀H + μ₀M
χ = (μ - 1)
μ = (1 + χ)
B = μ₀(H + M)
Magnetic field on axis of loop = μ₀I/(2r)
Magnetic field on perpendicular bisector of loop = μ₀I/(2πr³)³
Magnetic field due to solenoid = μ₀nI
Magnetic field due to toroid = μ₀nI/(2πr)
Force per unit length = μ₀I₁I₂/(2πr)

🪤 The 5 Mistakes That Cost Marks

Not using the correct formula for magnetic field due to a current carrying wire
Forgetting to consider the direction of magnetic field while calculating force on a current carrying wire
Not understanding the concept of magnetic moment and its relation to magnetic field
Incorrectly applying the formula for magnetic field due to a solenoid
Not considering the effect of magnetic field on a moving charge

✏️ 3 Solved PYQs

A current of 10 A is flowing ∈ a wire of length 1 m. The wire is placed ∈ a magnetic field of 0.1 T. If the angle between the wire and magnetic field is 30°, calculate the force acting on the wire.
- F = IL × B = 10 × 1 × 0.1 × s∈(30°) = 0.5 N
A solenoid of length 10 cm and radius 1 cm has 1000 turns. If a current of 5 A is flowing through it, calculate the magnetic field at its center.
- B = μ₀nI = 4π × 10⁻⁷ × 1000 × 5 = 0.0628 T
A bar magnet of magnetic moment 10 A m² is placed ∈ a magnetic field of 0.1 T. If the angle between the magnet and magnetic field is 60°, calculate the torque acting on the magnet.
- τ = MB s∈(θ) = 10 × 0.1 × s∈(60°) = 0.866 Nm

🧠 The One Thing Most Students Get Wrong

The concept of magnetic moment and its relation to magnetic field. Many students get confused between the two and end up using the wrong formula.

👁️ Ayush's Note

To solve problems related to magnetism, always start by identifying the given quantities and the unknown quantity.
Use the formula bank to find the relevant formula for the problem.
Always consider the direction of magnetic field and the angle between the wire and magnetic field while calculating force.
Practice problems regularly to develop a strong understanding of the concepts.

🔁 Last 5 Minutes Box

Revise the formula for magnetic field due to a current carrying wire.
Go through the concept of magnetic moment and its relation to magnetic field.
Practice a few problems related to force on a current carrying wire and magnetic field due to a solenoid.
Make sure to understand the concept of torque and its relation to magnetic moment.

📝 Practice MCQs

1. What is the magnetic field at the center of a solenoid of length 10 cm and radius 1 cm with 1000 turns, if a current of 5 A is flowing through it?

A) 0.01 T

B) 0.0628 T

C) 0.1 T

D) 1 T

Answer: B) 0.0628 T. Explanation: B = μ₀nI = 4π × 10⁻⁷ × 1000 × 5 = 0.0628 T

2. A current of 10 A is flowing ∈ a wire of length 1 m. The wire is placed ∈ a magnetic field of 0.1 T. If the angle between the wire and magnetic field is 30°, what is the force acting on the wire?

A) 0.1 N

B) 0.5 N

C) 1 N

D) 5 N

Answer: B) 0.5 N. Explanation: F = IL × B = 10 × 1 × 0.1 × s∈(30°) = 0.5 N

3. A bar magnet of magnetic moment 10 A m² is placed ∈ a magnetic field of 0.1 T. If the angle between the magnet and magnetic field is 60°, what is the torque acting on the magnet?

A) 0.5 Nm

B) 0.866 Nm

C) 1 Nm

D) 5 Nm

Answer: B) 0.866 Nm. Explanation: τ = MB s∈(θ) = 10 × 0.1 × s∈(60°) = 0.866 Nm

4. What is the magnetic field due to a current carrying loop of radius 1 m and current 5 A at a point on its axis at a distance of 2 m from its center?

A) 0.01 T

B) 0.0628 T

C) 0.1 T

D) 1 T

Answer: A) 0.01 T. Explanation: B = μ₀I/(2r) = 4π × 10⁻⁷ × 5/(2 × 2) = 0.01 T

5. A toroid of radius 10 cm and 1000 turns is carrying a current of 5 A. What is the magnetic field at its center?

A) 0.01 T

B) 0.0628 T

C) 0.1 T

D) 1 T

Answer: B) 0.0628 T. Explanation: B = μ₀nI/(2πr) = 4π × 10⁻⁷ × 1000 × 5/(2π × 0.1) = 0.0628 T

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides: