Syllabus Edition

First teaching 2023

First exams 2025

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Magnetic Force between Two Parallel Conductors (HL IB Physics)

Revision Note

Ann H

Author

Ann H

Expertise

Physics

Magnetic Force Between Two Parallel Conductors

  • A current carrying conductor, such as a wire, produces a magnetic field around it
  • The direction of the field depends on the direction of the current through the wire
    • This is determined by the right hand thumb rule

  • Parallel current-carrying conductors will therefore either attract or repel each other
    • If the currents are in the same direction in both conductors, the magnetic field lines between the conductors cancel out – the conductors will attract each other
    • If the currents are in the opposite direction in both conductors, the magnetic field lines between the conductors push each other apart – the conductors will repel each other

20.1 Same or opposite direction current_2

Both wires will attract if their currents are in the same direction and repel if in opposite directions

  • When the conductors attract, the direction of the magnetic forces will be towards each other
  • When the conductors repel, the direction of the magnetic forces will be away from each other
  • The magnitude of each force depends on the amount of current and the length of the wire

 

Force per Unit Length Between Two Parallel Conductors

  • The ratio F over L is the force per unit length between two parallel currents I1 and I2 separated by a distance
  • The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions
  • It is calculated using the equation:

F over L space equals space mu subscript 0 fraction numerator I subscript 1 I subscript 2 over denominator 2 straight pi r end fraction

  • Where:
    • F = the force applied between the two parallel wires (N)
    • = the length of each parallel conductor (m)
    • μ0 = the constant for the magnetic permeability of free space (4π × 10−7 N A−2)
    • I1 = the current through the first conducting wire (A)
    • I2 = the current through the second conducting wire (A)
    • = the separation between the two conducting wires (m)

T_fIGs2p_4-2-force-eqn-explanation

The forces on each of the current-carrying wires are equal and opposite in direction

Obtaining the Equation

  • The force from wire 2 on wire 1, F2B2I1Lsin(θ) 
  • In this situation the magnetic field is perpendicular to the current in the wire, so sin(θ) = 1
  • F2 = −F1 so the force between them is F
  • The force on a unit length of the wires is then given by F over L space equals space fraction numerator B subscript 2 I subscript 1 L over denominator L end fraction
    • Hence, F over L space equals space B subscript 2 I subscript 1
  • The magnitude of the magnetic field at a radial distance, away from the current conducting wire is: B space equals fraction numerator space mu subscript 0 I over denominator 2 pi r end fraction
    • In this case the magnetic field strength from B2 at a distance away from wire 2 is: B subscript 2 space equals space fraction numerator mu subscript 0 I subscript 2 over denominator 2 pi r end fraction
  • Substituting for B2 into the force per unit length equation gives us: F over L space equals space open parentheses fraction numerator mu subscript 0 I subscript 2 over denominator 2 pi r end fraction close parentheses I subscript 1

Worked example

Two long, straight, current-carrying conductors, WX and YZ, are held at a close distance, as shown in diagram 1.

The conductors each carry the same magnitude current in the same direction. A plan view from above the conductors is shown in diagram 2.

On diagram 2, draw arrows, one in each case, to show the direction of:

  • The magnetic field at X due to the current in wire YZ (label this arrow BYZ)
  • The force at X as a result of the magnetic field due to the current in the wire YZ (label this arrow FYZ)
  • The magnetic field at Y due to the current in wire WX (label this arrow BWX)
  • The force at Y as a result of the magnetic field due to the current in the wire WX (label this arrow FWX)

Answer:

Origin_of_the_Forces_Between_Current-Carrying_Conductors_Worked_example_-_Forces_on_Parallel_Conductor_Answer, downloadable AS & A Level Physics revision notes

  • Newton’s third law: When two bodies interact, the force on one body is equal but opposite in direction to the force on the other body
  • Therefore, the forces on the wires act in equal but opposite directions

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Ann H

Author: Ann H

Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.