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 :

Options

A. `15 A`
B. `5 A`
C. `13 A`
D. Information insufficient

Answer

C

Explanation

`int_(A)^(B)vec(B)_(P).vec(dl)=4mu_(0),int_(C)^(A)vec(B)_(Q).vec(dl)=-15 mu_(0)`
Now `int_(B)^(C)vec(B)_(P).vec(dl)` should be one third of `|int_(C)^(A)vec(B)_(Q).vec(dl)|`
So, `int_(B)^(C)vec(B)_(P).vec(dl)=5mu_(0)`, also `int_(C)^(A)vec(B)_(P).vec(dl)= int_(A)^(B)vec(B)_(P).vec(dl)=4mu_(0)`
Now, `int_(ABC)vec(B)_(P).vec(dl)=mu_(0)I`
`implies 4mu_(0)+5mu_(0)+4mu_(0)=mu_(0)I`
`implies I=13A`