If B is the magnetic field produced at the centre of a circular coil of one turn of length L carrying current I the what is the magnetic field at the centre of the same coil which is made into 10 turns ?

Explanation

For first circular coil , `B_(1) = B, n_(1) = 1, I_(1) = I, a_(1) = (L)/(2pi)`
For second circular coil, `B_(2) = ? N_(2) = 10, I_(2) = I, a_(2) = (L)/(2pi)`
As `B = (mu_(0) n I a^(2))/(2r), B prop n`.
`(B_(2))/(B_(1)) = (n_(2))/(n_(1))`
`(B_(2))/(B) = (10)/(1)`
`:. B_(2) = 10 B`