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

Explanation

Number of turns on the circular coil, `n = 100`
Radius of each turn, `r = 8.0 cm = 0.08 cm`
Current flowing in the coil, `I = 0.4A`
Magnitude of the magnetic field at the centre of the coil is given by the relations,
`|B| = (mu_(0))/(4pi) (2pi nI)/(r)`
Where,
`mu_(0) =` Permeability of free space
`=4n xx 10^(-7) TmA^(-1)`
`|B| = (4pi xx 10^(-7))/(4pi) xx (2pi xx 100 xx 0.4)/(0.08)`
`= 3.14 xx 10^(-4)T`
Hence the magnitude of the magnetic field is `3.14 xx 10^(-4)T`.