Two identical wires A and B , each of length l , carry the same current I . Wire A is bent into a circle of radius R and wire B is bent to form a square of side a . If B A and B B are the values of magnetic field at the centres of the circle and square respectively, then the ratio B A B B is

Step-by-step solution

As length of both the wires is same, 2 π R = 4 a ⇒ a R = 2 π 4 ⇒ a R = π 2 B A = μ 0 i 2 R and B B = μ 0 i π a 2 2 Therefore, ratio will be B A B B = μ 0 i 2 R × π a 2 2   μ 0 i = π a 4 2 R = π 4 2 π 2 = π 2 8 2