Magnetic Field and Torque?

📌 CONCEPT: The magnetic field inside a solenoid is given by the formula B = μ₀nI, where μ₀ is the magnetic constant, n is the number of turns per unit length, and I is the current flowing through the solenoid. The torque experienced by a bar magnet in a magnetic field is given by the formula τ = μB sinθ, where μ is the magnetic moment, B is the magnetic field strength, and θ is the angle between the magnetic moment and the magnetic field.

📐 RULE / FORMULA: The magnetic field inside a solenoid is given by B = μ₀nI and the torque experienced by a bar magnet is given by τ = μB sinθ.

💡 WORKED EXAMPLE: Given μ = 0.5 A·m², B = μ₀nI, I = 2 A, and n = 100 turns/m, we can calculate the magnetic field strength B = (4π × 10⁻⁷) × 100 × 2 = 2.512 × 10⁻³ T. Then, we can calculate the torque τ = 0.5 × 2.512 × 10⁻³ × sin90° = 1.256 × 10⁻³ Nm.

⚠️ COMMON MISTAKE: Students often forget to take into account the angle between the magnetic moment and the magnetic field, which is crucial in calculating the torque experienced by the bar magnet.