Magnetic Field of a Solenoid?

📌 CONCEPT: The magnetic moment of a solenoid is a measure of its ability to produce a magnetic field when used as a magnet, and it depends on the number of turns, the length of the solenoid, and the current flowing through it.

📐 RULE / FORMULA: The magnetic field (B) inside a solenoid is given by the formula B = μ₀nI, where μ₀ is the magnetic constant (4π × 10⁻⁷ Tm/A), n is the number of turns per unit length, and I is the current flowing through the solenoid. The magnetic moment (M) of a solenoid can be calculated using the formula M = nIA.

💡 WORKED EXAMPLE: Given a solenoid of 100 turns and length 0.1 m with a current of 2 A, and a magnetic field of 100 μT, we can calculate the magnetic moment as follows: M = nIA = (100 / 0.1 A/m) × 2 A = 2000 A/m². The magnetic moment is then M = B / (μ₀n) = (100 × 10⁻⁶ T) / (4π × 10⁻⁷ Tm/A × 100 A/m) = 2000 A/m².

⚠️ COMMON MISTAKE: Students often forget to convert the magnetic field from microtesla (μT) to tesla (T) and also misinterpret the units of the magnetic constant (μ₀).