A circular coil of one turn carries a current I. The same wire is then bent to from a smaller circular coil of 2 turns and the same current is passed through it. What is the relations between the fields at the centre of the coils in the second and first case ?

Options

A. `B_(2)=B_(1)`
B. `B_(2)=2B_(1)`
C. `B_(2)= (B_(1))/(2)`
D. `B_(2)=4B_(1)`

Answer

D

Explanation

`B_("centre") =(mu_(0))/(4pi ) ((2pinI)/(r))`
`As ((mu_(0))/(4pi)xx2piI)` is constant
`therefore B prop n/r therefore (B_(2))/(B_(1))=(n_(2))/(n_(1)) xx(r_(1))/(r_(2))" "...(1)`
The length of the coil is kept constant.
`therefore L (2pir_(1)) n_(1)= (2pir _(2))n _(2)`
`therefore (r _(1))/(r_(2))=(n_(2))/(n_(1))=2/1`
`therefore` From (1), `(B_(2))/(B_(1))=2/1 xx2/1 =4 therefore B_(2) =4B_(1)`