Force between parallel current-carrying conductors Evaluate the statement: “When two long, parallel conductors carry currents in the same direction, the force between them is repulsive.”

Introduction / Context:
The magnetic interaction between parallel currents is a cornerstone of electromagnetism and defines the ampere in classical terms. The direction of force depends on whether the currents are co-directional or counter-directional.

Given Data / Assumptions:

• Two long, straight, parallel conductors separated by distance r.
• Currents I1 and I2 flow in the same direction.
• Quasi-static fields; neglect edge effects.

Concept / Approach:

The magnetic field around conductor 1 at the location of conductor 2 is B1 = μ0 I1 /(2π r). Conductor 2 experiences magnetic force per unit length f = I2 × B1, direction given by the right-hand rule. For currents in the same direction, the force is attractive; for opposite directions, it is repulsive. Hence the given statement claiming repulsion for same-direction currents is false.

Step-by-Step Solution:

Verification / Alternative check:

Symmetry implies conductor 1 experiences equal and opposite force. This mutual attraction underpins the classical ampere definition and many busbar spacing calculations.

Why Other Options Are Wrong:

(c) direction does not depend on equality of currents; (d) AC does not change instantaneous force law (time-average remains attractive for in-phase currents); (e) sign is independent of spacing (magnitude changes with r).

Common Pitfalls:

Confusing magnetic force direction with electric force between like charges; here, current direction determines magnetic interaction.

Final Answer:

False