(455) Force between parallel wires [IB Physics SL/HL]

Force Between Parallel Wires

• Current Direction: Two parallel wires can either have currents in the same direction or in opposite directions.

Governing Equation

• Force Per Unit Length:

  • Formula: ( F/L = \frac{\mu_0 I_1 I_2}{2\pi r} )

  • ( F ): Force (Newtons)

  • ( r ): Distance between wires (meters)

  • ( I_1, I_2 ): Currents in the wires (amperes)

  • ( \mu_0 ): Permeability of free space ( = 4\pi \times 10^{-7} \text{ T m/A} )

Direction of Forces Using Right-Hand Rules

• Right-Hand Rule #1: Determining magnetic field (B)

  • Thumb: Direction of current

  • Fingers: Curl in direction of the magnetic field

• Right-Hand Rule #3: Determining force on wire

  • Fingertips: Direction of magnetic field

  • Thumb: Direction of current

  • Palm: Direction of force

Same Direction Currents

• Case: Currents in the same direction (I1 and I2 both upwards)

  • Wire 1 creates a magnetic field into the page at Wire 2.

  • Applying right-hand rule for wire 2:

    • Current: Up

    • B Field: Into the page

    • Force: To the left

  • Result: Attractive force between wires.

Opposite Direction Currents

• Case: Currents in opposite directions (I1 up, I2 down)

  • Wire 1 creates a magnetic field into the page at Wire 2.

  • Applying right-hand rule for wire 2:

    • Current: Down

    • B Field: Into the page

    • Force: To the right

  • Wire 1 responds similarly with a force to the left.

  • Result: Repulsive force between wires.

Conclusion

• Current in the same direction = Attractive Force

• Current in opposite directions = Repulsive Force

Mnemonic with Drake

• Drake represents attractive forces when currents are aligned, while he symbolizes repulsion for opposing currents.