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# A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

1. A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

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The magnitude of the magnetic field at the centre of a circular coil of radius r carrying current  I is given by,

$|B|=\frac{\mu _{0}I}{2r}$

For 100 turns, the magnitude of the magnetic field will be,

$|B|=100\times \frac{\mu _{0}I}{2r}$

$|B|=100\times \frac{4\pi \times 10^{-7}\times 0.4}{2\times 0.08}$        (current=0.4A, radius = 0.08m, permeability of free space = 4$\pi \times$10-7 TmA-1)

$=3.14\times10^{-4}T$

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