Three long straight parallel wires are kept as shown in the fig. The wire (3) carries a current I.
(i) The direction of flow of current I in wire (3) is such that the net force on wire (1) due to the other two wires, becomes zero.
What will be the direction of current I in the two cases ?
Also obtain the relation between the magnitude of currents `I_1, I_2 and I_3`.

Explanation

(i) Since net force per unit length on wire (1) due to other two wires is zero, the direction of `I_2 and I_3` must be mutually opposite and then `|vec(F_(12))| = |vec(F_(13))|`
`:. (mu_0 I_1I_2)/(2 pi d) = (mu_0 l_1 I)/(2 pi (2d)) implies I = 2I_(2)`
(ii) When direction of I of reversed then net force per unit length on wire (2) due to other two wires becomes zero. Hence, now `vec(F_21) + vec(F_23) = 0`
`:. |vecF_(21)| = |vecF_(23)| implies (mu_0 I_1 I_2)/(2 pi d) = (mu_0 I_2I)/(2 pi d) implies I_2 = I`