A wire of length l carries a steady current. It is bent first to form a circular plane loop of one turn. The magnetic field at the centre of the loop is B. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same is

Options

A. B
B. B/4
C. 4B
D. B/2

Answer

C

Explanation

The wire of length l is bent to from a circular loop, so `2pir=l`
`implies r=(l)/(2pi)`
The magnetic field at the centre of the loop is
`B=(mu_(0)I)/(2pi)=(mu_(0)Ixx2pi)/(2I)`
Now the same length of the wire is bent to from a double loop
`therefore 2 xx 2pir'=l`
`implies r'=(1)/(4pi)`
And the magnetic field at the centre
`B'=(mu_(0)Ixx2)/(2xxr')=(2mu_(0)I)/(2xx(1)/(4pi))=(2xx4pimuI)/(2I)`
`therefore (B')/(B)=4 implies B'=4B`