In the figure shown `W1` represent the cross section of an infinitely long wire carrying current I1 into the plane of the fig. AB is a line of length L and the wire `W1` is symmetrically located with respect to the line. The line integral `int_(A)^(B) vec(B).vec(d)l`. d l along the line from A to B is equal to – `a_(0)` where `a_(0)` is a positive number. Another long wire `W2` is placed symmetrically with respect to AB (see fig) and the value of `int_(A)^(B) vec(B).vec(d)l` becomes zero. Consider a line DC to the right of `W2`. The line is parallel to AB and has same length. The two wires fall on perpendicular bisector of both lines. If `int_C^D vec(B).vec(d)=2a_(0)` with both wires `W1` and `W2` present, calculate the ratio of current `I_(2) /I_(1)` in the two wires.

Answer

`I_(2)/I_(1)=1+sqrt(2)`