Analyse the interaction between two parallel current-carrying wires

Analyse the interaction between two parallel current-carrying wires

  • Wire with current gives magnetic field which exerts a force upon objects
  • 2 parallel wires with a current produce magnetic fields that affect each other
    • Same direction: fields attract and combine
    • Opposite: Fields repel each other
  • Use right hand grip (thumb – current, fingers – magnetic field) to determine direction and whether there will be attraction/repulsion

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  • The magnetic field strength at a distance d from the straight conductor carrying current I1 , can be found using the formula: magnetic-field-strength
  • If there is another straight conductor carrying current I , then this will interact with the magnetic field.


  • The force on wire carrying current I2 can be calculated using force-on-wire-carrying-current
  • The above equation is often re-written as force-on-wire-carrying-current-2
    • In the above equation:
      • F = force between conductors
      • I1 and I2 are the currents passing through the conductors
      • r is the distance between the conductors.
      • l is the length of the conductors
      • μo is the magnetic permeability of free space magnetic-permeability-of-free-space
    • Force is increased with longer wires and less distance between them

According to Newton’s third law “Every Action has an Equal and Opposite Reaction” . This can be explained as :

In a two-body system, if body X exerts a force on body Y, then body Y exerts a force on Body X that is equal in magnitude, but opposite in direction.

  • This means that the current I2 must exert an equal force on wire carrying current I1
  • This can be better explained through the idea that the magnetic field created by I2 must be interacting with wire carrying current I1  to exert a force upon it.


Thus the Force experienced by both the current carrying wires, is equal in magnitude but opposite in direction.

The definition Ampere (The S.I. unit for current) is based on this interacting force

  • One ampere is the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between those conductors a force equal to 2 × 10 −7 newtons per metre of length.
  • The Force is attractive if the current is in the same direction
  • The force is repulsive if the current is in opposite direction.

Extract from Physics Stage 6 Syllabus © 2017 NSW Education Standards Authority (NESA)