Force Between Two Parallel Current-Carrying Conductors
Calculates the force of attraction or repulsion between two long, parallel conductors carrying electric currents and its role in defining the Ampere.
What is Force Between Two Parallel Current-Carrying Conductors?
The SI unit of electric current. Defined as the constant current which, if maintained in two very long, straight, parallel conductors of negligible circular cross-section, placed one meter apart in vacuum, would produce between these conductors a force equal to 2 × 10⁻⁷ Newton per meter of length.
Key formula / rule: Force per unit length between two parallel conductors
Key points
- To understand the nature of the force between parallel current-carrying conductors.
- To derive and apply the formula for the force per unit length.
- To comprehend the experimental basis for the definition of the Ampere.
Common exam trap
Confusing attractive and repulsive forces based on current direction.
Definitions
- Term
Ampere (A)
- Meaning
The SI unit of electric current. Defined as the constant current which, if maintained in two very long, straight, parallel conductors of negligible circular cross-section, placed one meter apart in vacuum, would produce between these conductors a force equal to 2 × 10⁻⁷ Newton per meter of length.
- Term
Permeability of free space (μ₀)
- Meaning
A physical constant representing the measure of the ability of a vacuum to support the formation of a magnetic field. Its value is 4π × 10⁻⁷ T m/A.
Learning objectives
To understand the nature of the force between parallel current-carrying conductors.
To derive and apply the formula for the force per unit length.
To comprehend the experimental basis for the definition of the Ampere.
Formulae
- Name
Force per unit length between two parallel conductors
- Note
μ₀ is the permeability of free space (4π × 10⁻⁷ T m/A), I1 and I2 are the currents, and r is the distance between the conductors.
- Expression
F/L = (μ₀ * I1 * I2) / (2πr)
Prerequisites
Biot-Savart Law
Magnetic field due to a straight current-carrying conductor
Lorentz force on a current-carrying conductor in a magnetic field
Understanding of magnetic field lines and direction (Right-Hand Rule)
Common mistakes
Confusing attractive and repulsive forces based on current direction.
Forgetting the factor of 2π in the denominator of the formula.
Incorrectly applying the formula to non-parallel or finite-length conductors.
Not understanding the role of μ₀.
Keywords
Parallel conductors
Magnetic force
Current
Ampere
Permeability of free space
Attractive force
Repulsive force
Practice preview
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