Magnetic Field due to Current: Conceptual Dilemma?

📌 CONCEPT: The magnetic field due to a current-carrying wire is a region around the wire where magnetic forces can be detected.

📐 RULE / FORMULA: According to Ampere's Circuital Law, the magnetic field (B) due to a current-carrying wire is given by B = (μ₀ × I) / (2πr), where μ₀ is the magnetic constant, I is the current, and r is the distance from the wire.

💡 WORKED EXAMPLE: A long, straight wire carries a current of 10 A from east to west. For the circular wire of radius 5 cm, we have I = 10 A and r = 5 cm = 0.05 m. Using the formula, B = (4π x 10⁻⁷ Tm/A) x (10 A) / (2π x 0.05 m) = 4 x 10⁻⁴ T. For the long wire, B = (4π x 10⁻⁷ Tm/A) x (10 A) / (2π x 0.05 m) = 4 x 10⁻⁴ T. The magnetic fields at the point due to both the circular and long wires are equal.

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the magnetic field, which can be determined by the right-hand rule. They may also calculate the magnetic field using the wrong formula or forget to include the magnetic constant.