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

Step-by-step solution

The wire of length l is bent to from a circular loop, so 2 r=l r= l 2 The magnetic field at the centre of the loop is B= ₀ I 2 r = ₀ I 2 2 l Now the same length of the wire is bent to from a double loop aligned & 2 2 r^ =l & r^ = l 4 aligned And the magnetic field at the centre aligned & B^ = ₀ I 2 2 r^ = 2 ₀ I 2 l 4 = 2 4 I 2 l & B^ B =4 B^ =4 B aligned