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. unaltered
B. half of its value
C. double of its first value
D. four times of its first value

Answer

D

Explanation

`r_1=L/(2pi),r_2=(L/2)/(2pi)=L/(4pi) therefore r_2=R_1/2 but B=(mu_0)/(4pi)((2piI)/r)i.e Bpropto 1/r therefore` When r is reduced to half, the field becomes double and for 2 turns it will be 4B.