Along wire carries a steady current. It is bent into a circle of one tum and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of N tums. The magnetic field at the centre of the coil will be

Options

A. NB
B. `N^(2)`
C. 2NB
D. `2n^(2)B`

Answer

B

Explanation

Initially `r_(1)`=radius of coil = `l"/"2pi`
`:.B=(mu_(0)I)/(2r_(1))=(2mu_(0)Ipi)/(2l)`
Finally `R_(1)` =radius of coil`=(l)/(2piN)`
`:.B^(.)=(mu_(0)xxN)/(2r_(2))=(mu_(0)NIxx2piN)/(2l)=(2mu_(0)IN^(2)pi)/(2l)`
`:.B^(.)/(B)=(2mu_(0)IN^(2)pi)/(2l)xx(2l)/(2mu_(0)Ipi)=N^(2)`
`:.B^(.)=N^(2)B`