Magnetic Field of a Current Carrying Wire?
A long, straight wire carries a current of 20 A in a direction perpendicular to the plane of the paper. Two identical loops, each having a radius of 0.1 m, are placed symmetrically on either side of the wire. One loop is made of copper (conductivity = 5.8 × 10^7 S/m) and the other of a non-ferromagnetic material (conductivity = 3.0 × 10^7 S/m).
1 Answer
📌 CONCEPT: The magnetic field of a current-carrying wire is a vector field that surrounds the wire and is defined as the region around the wire where the force on a moving charge is zero and the force on a stationary charge is non-zero.
📐 RULE / FORMULA: The magnetic field (B) around a long, straight wire is given by B = μ₀I / (2πr), where μ₀ is the magnetic constant (4π × 10^(-7) Tm/A), I is the current in the wire, and r is the distance from the wire.
💡 WORKED EXAMPLE: To find the magnetic field at a distance of 0.1 m from a wire carrying a current of 20 A, we can use the formula B = μ₀I / (2πr). Substituting the values, we get B = (4π × 10^(-7) Tm/A × 20 A) / (2π × 0.1 m) = 4 × 10^(-5) T.
⚠️ COMMON MISTAKE: Students often forget to include the distance (r) in the formula or use the wrong value of the magnetic constant (μ₀).
21 Sept 26
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