A wire of length l is bent into a circular loop of radius R and carries a current I . The magnetic field at the centre of the loop is B . The same wire is now bent into a double loop of equal radii. If both loops carry the same current I and it is in the same direction, the magnetic field at the centre of the double loop will be

Step-by-step solution

Magnetic field at the centre of the loop For the wire which is looped double let radius becomes r Then, aligned l 2 & =2 r or l 4 & =(r) aligned array ll & B^ = ₀ 4 I 2 r 2 r^2 or & B^ = ₀ 4 I l 2 2 ( l 4 )^2 array Dividing Eq. (ii) by Eq. (iii), we get B^ B = ₀ 4 I l 16 ^2 l^2 ₀ 4 I l 4 ^2 l^2 array ll or & B^ B =4 or & B^ =4 B array