Force Between Two Parallel Currents

When current carrying conductor is placed in an external magnetic field B, the magnetic force on the conductor is given by :

F = I . (L x B)

Consider two parallel wires of equal length carrying a steady current :

1) The two wires will exert magnetic forces on each other.

2) Wire 1 will exert magnetic force on wire 2 and vice versa.

* The wires are separated by distance a and carry current I1 and I2 with same direction.

*Wire 2 that carrying current I2  set up the magnetic field B2 at position of wire 1

- The direction of magnetic field B2 is perpendicular to the wire.

- F1 =  F2 on 1 = I1 . (L x B2)

-Angle between L and B is 90 degree.

* The magnetic of B2 at every point of wire 1 is shown by equation below :

* Force 1, F2 on 1 is shown by equation :  F1 = I1 L x B2

*  Vector L and B is perpendicular to each other, so we can write :

p/s : IMPORTANT !!

(1)  To find the force on  a current-carrying wire due to a second current-carrying wire, first find the field due to the second wire at thew site of the first wire. Then find the force on the first wire due to that field.

(2) Parallel currents attract each other but anti parallel currents repel each other