A steady current is flowing through a long wire. If it is converted into a single turn circular coil, the magnetic field produced at its is B. Now it is converted into a circular coil having n tunrs. What will be the magnetic field at the centre of the coil ?

Explanation

Magnetic field a the centre of the single circular coil, `B=(mu_(0)I)/(2pi) `
If a coil of n turns is made, the radius reduces to `(r)/(m)`.
Thus the magnetic field at the centre of the coil
`=(mu_(0)nI)/(2*(r)/(n))=n^(2)*(mu_(0)I)/(2r)=n^(2)B`