Magnetic Field of a Solenoid

📌 CONCEPT: The magnetic field of a solenoid is uniform and directed along its axis, with its direction determined by the direction of the current flowing through it.

📐 RULE / FORMULA: The magnetic field (B) of a solenoid is given by the formula B = μ₀ * n * I, where μ₀ is the magnetic constant, n is the number of turns per unit length, and I is the current flowing through the solenoid.

💡 WORKED EXAMPLE: Given a solenoid with 200 turns per meter and a current of 5 A, the magnetic field at the compass would be B = μ₀ * 200 * 5. Assuming μ₀ = 4π * 10⁻⁷ Tm/A, B ≈ 3.14 * 10⁻⁴ T. Since the compass needle shows deflection, the direction of the magnetic field at the compass is along the axis of the solenoid, which is determined by the direction of the current flow. To produce a magnetic field of 0.5 T at the compass with the current doubled to 10 A, the number of turns per meter would be B = 0.5 / (μ₀ * 10), n ≈ 1.59 * 10⁴ turns per meter.

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the magnetic field at the compass, which is crucial in determining the direction of the current flow in the solenoid.