Three long straight parallel wires are kept as shown in figure. 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 other two wires, is zero (ii) By reversing the direction of I, the net force, on the wire (2) due to the other two wires, becomes zero.
What will be the directions of current I, in the two cases? Also obtain the relation between the magnitudes of current `I_1`, `I_2` and I.

Answer

(i) Downwards; `I=2I_2`
(ii) upwards; `I=I_1`

Explanation

(i) The net force on wire (1) well be zero if the force on wire (1) due to wire (2) is equal and opposite to the force on wire (1) due to wire (3). It is so when current direction in wire (3) is downwards. Then
`(mu_0)/(4pi)(2I_1I_2)/(a)=(mu_0)/(4pi)(2I_1I)/((a+a))` or `I=2I_2`
(ii) When the direction of current in wire (3) is reversed, i.e., in upwards direction, figure, then the net force on wire (2) will be zero if force on wire (2) due to wire (1) is equal and opposite to the force on wire (2) due to wire (3), i.e.,

`(mu_0)/(4pi)(2I_1I_2)/(a)=(mu_0)/(4pi)(2II_2)/(a)` or `I=I_1`