A circular coil consisting of 200 turns has a radius of 10 cm and carries a current of 2.0 A . Determine the magnitude of the magnetic field B at the centre of the coil.

Step-by-step solution

The magnetic field at the centre of a circular coil of N turns is given by: B = ₀ N I 2R Given parameters: N = 200 R = 10 cm = 0.1 m I = 2.0 A ₀ = 4 10⁻⁷ T m/A Substituting the values into the formula: B = 4 10⁻⁷ 200 2.0 2 0.1 B = 1600 10⁻⁷ 0.2 B = 8000 10⁻⁷ T B = 8 10⁻⁴ T Using 3.14 : B = 8 3.14 10⁻⁴ T B = 25.12 10⁻⁴ T B = 2.51 10⁻³ T = 2.51 mT