Physics

Physics

Problem

A flat circular coil of 50 turns and radius 5 cm5\,\text{cm} carries a steady current of 3 A3\,\text{A}. Calculate the magnitude of the magnetic field at the centre of the coil. (Take μ0=4π×10−7 T m A−1\mu_0 = 4\pi \times 10^{-7}\,\text{T m A}^{-1}.) a) 7.5×103 μT7.5 \times 10^{3}\,\mu\text{T} b) 9.4×102 μT9.4 \times 10^{2}\,\mu\text{T} c) 1.9×103 μT1.9 \times 10^{3}\,\mu\text{T} d) 3.8×103 μT3.8 \times 10^{3}\,\mu\text{T}
Intuitive explanation

This problem asks you to find the magnetic field created by a current loop at its geometric center—a classic application of the Biot-Savart law simplified to a clean formula. The key insight is that every segment of the circular wire contributes a field pointing in the same direction (perpendicular to the coil's plane), so you just add up all contributions without worrying about cancellation. With multiple turns, each loop adds its field, making the total proportional to the number of turns.

Intuitive explanation

This problem asks you to find the magnetic field created by a current loop at its geometric center—a classic application of the Biot-Savart law simplified to a clean formula. The key insight is that every segment of the circular wire contributes a field pointing in the same direction (perpendicular to the coil's plane), so you just add up all contributions without worrying about cancellation. With multiple turns, each loop adds its field, making the total proportional to the number of turns.

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