A length of wire carries a steady current I. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give double loop of smaller radius. If the same current I is passed, the ratio of the magnitude of magnetic field at the centre with its first value is:

Options

A. a quarter of its first value
B. unaltered
C. four times of its first value
D. a half of its first value

Answer

C

Explanation

`L=2pir_(1) implies r_(1)=L//2pi`
`B_(0)=(mu_(0)NI)/(2r_(1))=(mu_(0)I)/(2.L/(2pi))=(mu_(0)Ipi)/L`

`L=2.2pir_(2) = gt r_(2) =L//4pi`
`B'_(0)=(mu_(0)NI)/(2r_(2))=(mu_(0)xx@I)/(2.L/(4pi))=(4mu_(0)Ipi)/L`
`(B'_(0))/(B_(0))=4`