Question Detail
Question
A magnetic induction of 20μT is applied to a long straight current-carrying wire. If the measurement is taken at a distance (radius) of 120mm from the wire, find the current in the wire. Take μ₀ = 4π × 10⁻⁷ Tm/A.
Correct Answer
Option C is the correct answer.
Detailed Explanation
The magnetic field (B) due to a long straight current-carrying wire is given by the formula: B = (μ₀ * I) / (2π * r).We are given: B = 20 μT = 20 × 10⁻⁶ T, r = 120 mm = 0.12 m, μ₀ = 4π × 10⁻⁷ Tm/A.Rearranging the formula to find the current (I):I = (B * 2π * r) / μ₀I = (20 × 10⁻⁶ T * 2π * 0.12 m) / (4π × 10⁻⁷ Tm/A)I = (20 × 10⁻⁶ * 2 * 0.12) / (4 × 10⁻⁷)I = (4.8 × 10⁻⁶) / (4 × 10⁻⁷)I = (4.8 / 4) × (10⁻⁶ / 10⁻⁷)I = 1.2 × 10¹ = 12 A.
Hint
Use Ampere's law for a long straight wire: B = (μ₀I) / (2πr). Ensure units are consistent (meters, Tesla).