Force Between Two Parallel Current Carrying Conductor

Description:

Two current carrying straight conductors placed near each other will exert (magnetic) forces on each other due to magnetic field of each other.

Figure shows two long parallel conductors separated by a distance d and bearing currents i_a and i_b. The conductor ‘a’ produces a magnetic field B_a at all points along the conductor ‘b’. The right-hand rule tells us that the direction of this field is downwards. Its magnitude is given by

The conductor ‘b’ will experience a sideways force on account of the external field B_a. The direction of this force is towards the conductor ‘a’. you can verify this either by the cross product rule of vectors or by Fleming’s left hand rule. We label this force F_ba, the force on a segment L of ‘b’ due to ‘a’. The magnitude of this force is given by,

F_ba = i_aIB_a

From considerations similar to above we can find that the force F_ab, on a segment of length L of ‘a’ due to the current in ‘b’ is equal in magnitude to ‘b’ and directed towards ‘b’.

Note −  Parallel current carrying wires attract, and anti-parallel current carrying wires repel each other.