A closely packed flat circular coil has 100 turns and a diameter of 10 cm . If the magnetic field produced at the centre of the coil is 8 10⁻⁴ T , what is the magnitude of the current flowing through it? (Take permeability of free space ₀ = 4 10⁻⁷ T m/A )

Step-by-step solution

Let the diameter of the coil be D = 10 cm = 0.1 m . The magnetic field at the centre of a circular coil of N turns is given by: B = ₀ N I 2R Since 2R = D , the formula can be written as: B = ₀ N I D Rearranging for the current I : I = B D ₀ N Substituting the given values: I = 8 10⁻⁴ 0.1 4 10⁻⁷ 100 I = 0.8 10⁻⁴ 4 10⁻⁵ I = 8 10⁻⁵ 4 10⁻⁵ = 2 A Answer: 2 A